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)

1 answer

To find the length of the ramp, we can use the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

In this case, the ramp will form a right triangle with the height and length of the cage. So the length of the ramp, which is the hypotenuse, can be found using the formula:

ramp_length^2 = height^2 + length^2

Substituting the given values:

ramp_length^2 = 50^2 + 70^2

ramp_length^2 = 2500 + 4900

ramp_length^2 = 7400

Taking the square root of both sides:

ramp_length = √7400

ramp_length ≈ 86 cm

Therefore, the ramp needs to be approximately 86 cm long to fit diagonally in the cage.