Are these practice questions for The Baudhayana-Pythagoras Theorem based on the CBSE pattern?

Yes. Every practice question is modeled on the CBSE Class 8 Mathematics exam pattern — including MCQs, assertion-reason questions, and short-answer formats that frequently appear in CBSE papers.

Are the practice questions for The Baudhayana-Pythagoras Theorem free?

Yes. Every chapter includes free practice questions for Class 8 students to get you started.

What types of questions are included?

The practice set for The Baudhayana-Pythagoras Theorem mainly includes MCQs and CBSE-style short-answer questions, with instant feedback on each answer. For full-length textbook practice, use the NCERT Solutions page.

Are the practice questions suitable for board exam preparation?

Yes. The questions test the same concepts and depth that CBSE asks in board exams. After finishing, also solve the NCERT and NCERT Exemplar exercises for The Baudhayana-Pythagoras Theorem for full coverage.

How many practice questions are there for The Baudhayana-Pythagoras Theorem?

The number scales with chapter length and concept density. Each chapter typically has 15-50 practice questions across MCQ and short-answer formats.

The Baudhayana-Pythagoras Theorem Class 8 Mathematics Practice Questions with Answers

easy

In a right-angled triangle

\triangle XYZ

, the right angle is at vertex

Y

. Identify the hypotenuse of this triangle.

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easy

In a right-angled triangle, the hypotenuse is 29 cm long and one of the shorter sides is 20 cm. Calculate the length of the third side.

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easy

Explain why simply doubling the side length of a square does not result in a square with double the area. Use an example to support your explanation.

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easy

Justify why doubling the side length of a square results in an area that is four times, not two times, the original area.

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easy

Define a 'Baudhāyana triple'.

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easy

State the Baudhāyana-Pythagoras theorem using the variables

a, b,

and

c

for the sides of a right-angled triangle.

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easy

Analyze if the set of lengths (9 cm, 40 cm, 41 cm) can form the sides of a right-angled triangle.

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easy

A rectangular screen has a length of 16 inches and a width of 12 inches. Calculate the length of its diagonal.

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easy

Without constructing the triangle, justify that a triangle with side lengths 9 cm, 40 cm, and 41 cm must be a right-angled triangle.

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easy

Critique the following statement: 'The triple

(1, 2, \sqrt{5})

is a Baudhāyana triple because

1^2 + 2^2 = (\sqrt{5})^2

'.

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easy

Calculate the length of the hypotenuse of an isosceles right-angled triangle whose equal sides are 5 cm each.

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easy

Examine if a triangle with side lengths 8 cm, 10 cm, and 13 cm is a right-angled triangle.

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easy

Evaluate the statement: 'If

(a, b, c)

is a primitive Baudhāyana triple, then

(ka, kb, kc)

is also a primitive triple for any integer

k > 1

.' Justify your answer.

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medium

An equilateral triangle has a side length of '

s

' units. Derive a formula for its height (

h

) and then formulate an expression for its area in terms of '

s

'.

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medium

State Fermat's Last Theorem and name the mathematician who is credited with its proof.

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medium

Calculate the side length of a square whose area is half the area of a larger square with a side length of 10 m.

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medium

A 10 m long ladder is placed against a vertical wall. The foot of the ladder is 6 m away from the base of the wall. Calculate the height the ladder reaches on the wall.

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medium

Formulate a proof that the diagonals of a rhombus are perpendicular bisectors of each other. Then, derive the formula

4s^2 = d_1^2 + d_2^2

, relating the side length (

s

) of the rhombus to the lengths of its diagonals (

d_1

and

d_2

).

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medium

List two different examples of primitive Baudhāyana triples.

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medium

Describe in detail Baudhāyana's method for combining two squares of different sizes to create a single larger square whose area is the sum of the two.

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medium

Recall the relationship between the equal sides '

a

' of an isosceles right triangle and its hypotenuse '

c

'.

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medium

One leg of a right-angled triangle is 12 cm and its hypotenuse is 15 cm. Calculate the perimeter of the triangle.

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medium

A person starts from a point, walks 9 km due East, and then 12 km due North. Calculate the shortest distance from the starting point to the final position.

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medium

Design a geometric procedure to construct a square whose area is equal to the difference between the areas of two given squares with side lengths

b

and

a

(where

b > a

). Provide a step-by-step construction and a formal proof to justify your method.

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medium

Calculate the side length of a square whose area is the sum of the areas of two squares with side lengths 8 cm and 15 cm respectively.

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medium

Justify whether the primitive Baudhāyana triple

(8, 15, 17)

can be generated using the odd-square method described in the text, which produces triples where the hypotenuse and one leg are consecutive integers.

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medium

Two vertical poles of heights 11 m and 6 m stand on level ground. The distance between their feet is 12 m. Calculate the distance between their tops.

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medium

Explain the difference between a primitive and a non-primitive Baudhāyana triple. Give one example of each.

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medium

Design a step-by-step geometric construction to create a square whose area is equal to the sum of the areas of three given squares with side lengths

a, b,

and

d

. Justify your method.

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medium

The triple (7, 24, 25) is a primitive Baudhāyana triple. Apply a scaling factor of 3 to generate a new Baudhāyana triple and verify the result.

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medium

Describe the geometric construction given by Baudhāyana to create a square with exactly double the area of a given square.

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medium

Propose the first two geometric steps to construct a line segment of length

\sqrt{3}

units, starting with only a straightedge, a compass, and a given line segment of length 1 unit.

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medium

Summarize the argument that explains why the square root of 2,

\sqrt{2}

, cannot be a number with a terminating decimal representation.

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hard

The diagonals of a rhombus measure 14 cm and 48 cm. Calculate the perimeter of the rhombus.

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hard

The hypotenuse of an isosceles right-angled triangle is

\sqrt{98}

m. Calculate the length of its two equal sides.

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hard

Recall the paper-folding method for constructing a square with half the area of a given square. Explain why this method works.

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hard

Create a word problem involving a ship's mast. A rope is tied to the top of the mast. Initially, the rope is taut and staked to the deck 9 meters from the base of the mast. The rope is then pulled in by 3 meters, and it is now staked to the deck at a new position. The mast is 12 meters tall. Create and solve an equation to find how far the new stake point is from the base of the mast.

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hard

A wire is stretched from the top of a 9 m pole to the top of a 16 m pole. If the poles are 24 m apart, solve for the length of the wire.

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hard

A student uses the diagram from Baudhāyana's proof for combining two different squares, which involves arranging four congruent right triangles (legs

a, b

; hypotenuse

c

) to form a large square. Critique their argument by justifying the unstated assumption that the inner quadrilateral formed by the four hypotenuses is a square.

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hard

A rectangle with integer side lengths

a

and

b

is inscribed in a circle. Create a formula for the square of the circle's diameter,

D^2

. Then, prove that if a square is also inscribed in the same circle, the area of this inscribed square will be an integer if and only if

a^2 + b^2

is an even number.

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hard

Explain the method of generating Baudhāyana triples using the sum of consecutive odd numbers. Demonstrate this method by using the odd square number 49.

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hard

Summarize the two arguments provided in the text that explain why the number

\sqrt{2}

is irrational.

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hard

If

(a, b, c)

is a Baudhāyana triple, explain why

(ka, kb, kc)

is also a Baudhāyana triple for any positive integer

k

.

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hard

Evaluate whether

\sqrt{12}

can be expressed as a fraction

\frac{m}{n}

where

m

and

n

are co-prime integers. Formulate a proof by contradiction, using the property of prime factors in square numbers.

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The Baudhayana-Pythagoras TheoremClass 8 Mathematics Practice Questions