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

78.6 cm
78.6 cm

116.3 cm
116.3 cm

92.9 cm

1 answer

To find the length of the ramp, we need to find the diagonal length of the rectangular prism. This can be done using the formula for the diagonal of a rectangular prism:

diagonal = square root of (length^2 + width^2 + height^2)

Plugging in the given values, we get:

diagonal = square root of (70^2 + 35^2 + 50^2)
diagonal = square root of (4900 + 1225 + 2500)
diagonal = square root of (8625)
diagonal ≈ 92.9 cm.

Therefore, the length of the ramp should be approximately 92.9 cm.