Melissa has a gerbil that lives in a cage in the shape of a rectangular prism. She wants to put a ramp in the cage to give her gerbil exercise. The cage has a length of 70 cm, a width of 35 cm, and a height of 50 cm. How long does the ramp need to be to fit diagonally in the cage? Round the answer to the nearest tenth.(1 point)

1 answer

To find the length of the ramp, we can use the Pythagorean theorem.

The diagonal of the cage can be found by finding the diagonal of the base, which is a rectangle with length 70 cm and width 35 cm, and the height of the cage. The diagonal D can be found using the formula

D = √(L^2 + W^2 + H^2),

where L is the length, W is the width, and H is the height of the prism.

Substituting the given values, we get

D = √(70^2 + 35^2 + 50^2)
= √(4900 + 1225 + 2500)
= √(8625)
≈ 92.9 cm

Therefore, the ramp needs to be approximately 92.9 cm long, rounded to the nearest tenth.