The Baudhayana-Pythagoras TheoremClass 8 Mathematics Case Study Questions
10 Questions
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Case 1 of 10
Case Study7 marks
The Firefighter's Ladder
A firefighter is rescuing a cat stuck on a tree branch. He uses a ladder that is m long. For stability and safety, the base of the ladder is placed m away from the base of the tree, which is standing vertically on level ground. This setup creates a right-angled triangle, with the ladder acting as the hypotenuse, the tree as the vertical side, and the ground as the horizontal base. The firefighter needs to know the height the ladder reaches to ensure it is tall enough for the rescue.
Questions on this case
1(1 mark)MCQ
In the right-angled triangle formed, what does the 13 m length of the ladder represent?
2(1 mark)
Calculate the height on the tree that the top of the ladder reaches.
3(1 mark)MCQ
If the firefighter moves the base of the ladder so it is now 12 m from the tree, what new height will it reach?
4(2 marks)
Is it possible for this 13 m ladder to reach a height of 14 m on the tree? Justify your answer.
5(2 marks)
Another firefighter arrives with a 15 m ladder and places its base 9 m from the tree. Which ladder reaches higher up the tree, the first one in its original position or the second one?
Case Study7 marks
Ship's Journey
A cargo ship leaves a port and sails km due East. After reaching a waypoint, it changes its course and sails km due North to reach its final destination, a remote island. The ship's captain wants to know the direct, straight-line distance between the starting port and the island, as this is the path a helicopter would take. The ship's journey can be visualized as two perpendicular sides of a right-angled triangle, with the direct path being the hypotenuse.
Questions on this case
1(1 mark)MCQ
The ship's path forms a right-angled triangle. What are the lengths of the two shorter, perpendicular sides?
2(1 mark)
Calculate the direct, straight-line distance from the starting port to the island.
3(2 marks)MCQ
On the return journey, the ship sails directly from the island back to the port. How much shorter is this direct return journey compared to the original path the ship took to get to the island?
4(1 mark)
A second ship travels 12 km East and then 16 km North from the same port. What is its direct distance from the port?
5(2 marks)
If the first ship had only enough fuel to travel a total of 40 km, could it complete a journey of 12 km East, then 16 km North, and then return directly to the port? Justify your answer.
Case Study7 marks
Designing a Rectangular Park
A city planner is designing a new rectangular park with a length of m and a width of m. A straight gravel path is to be built connecting two opposite corners of the park, forming the diagonal. This path will allow people to take a shortcut across the park. The planner needs to calculate the length of this path to order the correct amount of gravel. The rest of the park, excluding the path, will be covered in grass. The entire park also needs to be fenced.
Questions on this case
1(1 mark)MCQ
The diagonal path, along with the length and width of the park, forms which type of triangle?
2(1 mark)
What is the length of the gravel path?
3(2 marks)MCQ
A person walks along the edges of the park (one length and one width) to get from one corner to the opposite one. How much farther do they walk compared to someone using the diagonal path?
4(1 mark)
The planner considers an alternative design for a square park that has the same perimeter as the original rectangular park. What would be the side length of this square park?
5(2 marks)
What is the area of a square whose diagonal is 10 m long?