Question
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
116.3 cm
116.3 cm
92.9 cm
92.9 cm
60.2 cm
60.2 cm
78.6 cm
78.6 cm
To find the length of the ramp, we need to find the diagonal of the rectangular prism. We can use the formula for the diagonal of a rectangular prism, which is:
diagonal = √(length^2 + width^2 + height^2)
Plugging in the given values, we have:
diagonal = √(70^2 + 35^2 + 50^2)
= √(4900 + 1225 + 2500)
= √(8625)
≈ 92.9 cm
So, the correct answer is 92.9 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 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 form the two sides of the right triangle, and the ramp will act as the hypotenuse.
Using the Pythagorean theorem, we can calculate the length of the ramp as follows:
Length of the ramp = √(Length of the cage^2 + Width of the cage^2)
Length of the ramp = √(70^2 + 35^2)
Length of the ramp = √(4900 + 1225)
Length of the ramp = √6125
Length of the ramp = 78.6 cm (rounded to the nearest tenth)
Therefore, the ramp needs to be approximately 78.6 cm long to fit diagonally in the cage.
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 side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the length and width of the cage form a right triangle, and the diagonal of the cage represents the hypotenuse. Therefore, we can use the Pythagorean theorem to find the length of the ramp.
Let's calculate it step by step:
1. Square the length and the width of the cage:
Length^2 = 70^2 = 4900
Width^2 = 35^2 = 1225
2. Add the squares of the length and width:
4900 + 1225 = 6125
3. Take the square root of the sum to find the length of the diagonal (hypotenuse):
√6125 ≈ 78.350
Rounded to the nearest tenth, the length of the diagonal is approximately 78.4 cm.
Therefore, the ramp needs to be approximately 78.4 cm long to fit diagonally in the cage.