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.

Answer 1

To find the length of the ramp, we need to use the Pythagorean theorem to find the length of the diagonal of the rectangular prism.

First, we find the diagonal of the base of the rectangular prism using the Pythagorean theorem:

diagonal = √(length^2 + width^2)
diagonal = √(70^2 + 35^2)
diagonal = √(4900 + 1225)
diagonal = √6125
diagonal ≈ 78.2 cm

Next, we find the diagonal height of the rectangular prism:

diagonal height = √(diagonal^2 + height^2)
diagonal height = √(78.2^2 + 50^2)
diagonal height = √(6102.25 + 2500)
diagonal height = √(8602.25)
diagonal height ≈ 92.8 cm

Therefore, the ramp needs to be approximately 92.8 cm long.

Answer 2

1. 15.0ft
2. 58.5cm
3. 8.8cm
4. 9.1m
5. 92.9