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
92.9 cm
92.9 cm
60.2 cm
60.2 cm
116.3 cm
116.3 cm
78.6 cm
A. 15.0 ft
B 59.5
C 8.8 cm
D 9.1
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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 side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this problem, the length and the width of the rectangular prism form the two sides of the right triangle, and the diagonal of the rectangular prism (which represents the length of the ramp) is the hypotenuse.
Using the Pythagorean theorem, we can calculate the length of the diagonal as follows:
Diagonal^2 = Length^2 + Width^2
Diagonal^2 = 70^2 + 35^2
Diagonal^2 = 4900 + 1225
Diagonal^2 = 6125
Diagonal ≈ √6125
Diagonal ≈ 78.6 cm
Therefore, the ramp needs to be approximately 78.6 cm long to fit diagonally in the cage.