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)
Responses
116.3 cm
116.3 cm
78.6 cm
78.6 cm
60.2 cm
60.2 cm
92.9 cm
To find the length of the ramp, we need to find the diagonal of the rectangular prism.
Using the Pythagorean theorem, we can calculate the length of the ramp as follows:
diagonal^2 = length^2 + width^2 + height^2
diagonal^2 = 70^2 + 35^2 + 50^2
diagonal^2 = 4900 + 1225 + 2500
diagonal^2 = 8625
Taking the square root of both sides:
diagonal = √8625
diagonal ≈ 92.9 cm
Therefore, the length of the ramp needs to be approximately 92.9 cm.