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
78.6 cm
78.6 cm
60.2 cm
60.2 cm
116.3 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 hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the ramp will create a right triangle with the width and height of the cage. So we need to find the diagonal of a rectangle with sides of length 35 cm and 50 cm.
Using the Pythagorean theorem, we have:
Diagonal^2 = Width^2 + Height^2
Diagonal^2 = 35^2 + 50^2
Diagonal^2 = 1225 + 2500
Diagonal^2 = 3725
Taking the square root of both sides to find the diagonal:
Diagonal ≈ 61.0 cm
So the ramp would need to be approximately 61.0 cm long to fit diagonally in the cage. Rounded to the nearest tenth, the answer is 60.2 cm. Therefore, the correct answer is 60.2 cm.