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.
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 longest side) is equal to the sum of the squares of the other two sides.
In this case, the length and height of the cage represent the other two sides of the right triangle, and we need to find the length of the diagonal (the hypotenuse).
Using the Pythagorean theorem, we can calculate the length of the diagonal as follows:
Diagonal^2 = Length^2 + Height^2
Diagonal^2 = 70 cm^2 + 50 cm^2
Diagonal^2 = 4900 cm^2 + 2500 cm^2
Diagonal^2 = 7400 cm^2
To find the length of the diagonal (the ramp), we take the square root of both sides:
Diagonal = √(7400 cm^2)
Diagonal ≈ 86 cm
Therefore, the length of the ramp needs to be approximately 86 cm.