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
92.9 cm
92.9 cm
60.2 cm
60.2 cm
116.3 cm
To find the length of the ramp needed to fit diagonally in the cage, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the length and width of the cage represent the two sides of the right triangle, and the ramp represents the hypotenuse.
Using the formula:
c^2 = a^2 + b^2
where c is the length of the ramp and a and b are the length and width of the cage:
c^2 = 70^2 + 35^2
c^2 = 4900 + 1225
c^2 = 6125
Taking the square root of both sides:
c = sqrt(6125)
c ≈ 78.6 cm
Therefore, the length of the ramp needed to fit diagonally in the cage is approximately 78.6 cm.