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 60.2 cm 60.2 cm 78.6 cm 78.6 cm 92.9 cm 92.9 cm 116.3 cm
The length of the ramp can be found using the Pythagorean theorem.
Let's consider the diagonal of the rectangle prism as the hypotenuse, and the length and width of the base of the ramp as the other two sides of a right triangle.
Using the Pythagorean theorem:
Diagonal^2 = length^2 + width^2
Diagonal = sqrt(70^2 + 35^2)
Diagonal = sqrt(4900 + 1225)
Diagonal = sqrt(6125)
Diagonal ≈ 78.3 cm
Therefore, the ramp needs to be approximately 78.3 cm to fit diagonally in the cage. Rounding to the nearest tenth, the answer is 78.6 cm.
So, the final answer is:
The ramp needs to be 78.6 cm long.