Question

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)60.2 cm116.3 cm78.6 cm92.9 cm

Explanation:

Step1: Find base diagonal length

First, calculate the diagonal of the rectangular base using the Pythagorean theorem. Let $l=70$ cm, $w=35$ cm.
$$d_{base} = \sqrt{l^2 + w^2} = \sqrt{70^2 + 35^2}$$
$$d_{base} = \sqrt{4900 + 1225} = \sqrt{6125}$$

Step2: Find space diagonal length

Use the base diagonal and height $h=50$ cm to find the 3D space diagonal (ramp length) with the Pythagorean theorem.
$$d_{space} = \sqrt{d_{base}^2 + h^2} = \sqrt{6125 + 50^2}$$
$$d_{space} = \sqrt{6125 + 2500} = \sqrt{8625} \approx 92.9$$

Answer:

D. 92.9 cm