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
78.6 cm
78.6 cm
60.2 cm
60.2 cm
92.9 cm
92.9 cm
116.3 cm
To find the length of the ramp, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the diagonal side) is equal to the sum of the squares of the other two sides.
Using the length, width, and height of the cage as the two sides of the right triangle, we can calculate the length of the diagonal (ramp) as follows:
Length of ramp = sqrt((length^2) + (width^2) + (height^2))
Length of ramp = sqrt((70^2) + (35^2) + (50^2))
Length of ramp = sqrt(4900 + 1225 + 2500)
Length of ramp = sqrt(8625)
Length of ramp ≈ 92.9 cm
Therefore, the length of the ramp needs to be approximately 92.9 cm.