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

116.3 cm
116.3 cm

60.2 cm
60.2 cm

92.9 cm
92.9 cm

92.9 cm

how

To find the length of the ramp needed to fit diagonally in the cage, we need to calculate the diagonal of the rectangular prism formed by the dimensions of the cage (length, width, and height).

The formula for calculating the diagonal of a rectangular prism is:

diagonal = √(length^2 + width^2 + height^2)

Given:
Length = 70 cm
Width = 35 cm
Height = 50 cm

Now, plug in these values into the formula:

diagonal = √(70^2 + 35^2 + 50^2)
diagonal = √(4900 + 1225 + 2500)
diagonal = √(8625)
diagonal ≈ 92.9 cm

Therefore, the ramp needs to be approximately 92.9 cm long to fit diagonally in the cage.