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
A
116.3 cm
B
92.9 cm
C
78.6 cm
D
60.2 cm
To find the length of the ramp, we need to find the diagonal of the rectangle formed by the length and width of the cage. We can use the Pythagorean theorem to find this diagonal.
Using the Pythagorean theorem, we have:
diagonal^2 = length^2 + width^2
diagonal^2 = (70 cm)^2 + (35 cm)^2
diagonal^2 = 4900 cm^2 + 1225 cm^2
diagonal^2 = 6125 cm^2
Taking the square root of both sides, we get:
diagonal = √(6125 cm^2)
diagonal ≈ 78.6 cm
Therefore, the correct answer is C) 78.6 cm.