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)

To find the length of the ramp that fits diagonally in the cage, we can use the Pythagorean theorem in three dimensions. The formula to find the diagonal \(d\) of a rectangular prism is: \[ d = \sqrt{l^2 + w^2 + h^2} \] Where \(l\) is the length, \(w\) is the width, and \(h\) is the height of the cage. Plugging in Melissa’s numbers: \[ d = \sqrt{70^2 + 35^2 + 50^2} \] Calculating each part: - \(70^2 = 4900\) - \(35^2 = 1225\) - \(50^2 = 2500\) Now, add them together: \[ 4900 + 1225 + 2500 = 8625 \] Now take the square root: \[ d = \sqrt{8625} \approx 92.9 \text{ cm} \] So, the ramp needs to be approximately **92.9 cm** long to fit diagonally in the cage.