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.
a.92.9 cm
b.60.2 cm
c.78.6 cm
d.116.3 cm
To find the length of the ramp, we need to calculate the diagonal of the rectangular prism shaped cage. We can use the formula for the diagonal of a rectangular prism, which is given by:
diagonal = √(length^2 + width^2 + height^2)
Plugging in the values from the problem, we have:
diagonal = √(70^2 + 35^2 + 50^2)
= √(4900 + 1225 + 2500)
= √(8625)
≈ 92.9 cm
So the length of the ramp needs to be approximately 92.9 cm, which corresponds to option a.