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 his gerbil exercise. The cage has the 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. Are you available? Responses are: 92.9 cm. 116.3 cm. 78.6 cm. Or 60.2 cm
The length of the ramp can be calculated using the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's denote the length of the ramp as x. The two other sides of the right triangle are the height (50 cm) and the diagonal of the rectangular prism (which can be found using the diagonal of a rectangle formula: √(length^2 + width^2)).
Diagonal of the rectangle = √(70^2 + 35^2) = √(4900 + 1225) = √6125 ≈ 78.3 cm
Using the Pythagorean theorem, we have:
x^2 = 50^2 + 78.3^2
x^2 = 2500 + 6123.09
x^2 = 8623.09
x ≈ √8623.09
x ≈ 92.9 cm
Therefore, the correct answer is 92.9 cm.