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. 15.0ft
2. 58.5cm
3. 8.8cm
4. 9.1m
5. 92.9
To find the length of the ramp, we need to find the diagonal of the rectangular prism. We can use the Pythagorean Theorem to do this.
The Pythagorean Theorem states that the square of the length of the hypotenuse (diagonal in this case) of a right triangle is equal to the sum of the squares of the other two sides.
Let's label the length, width, and height as follows:
Length (L) = 70 cm
Width (W) = 35 cm
Height (H) = 50 cm
Now we can calculate the length of the diagonal (D) using the Pythagorean Theorem:
D^2 = L^2 + W^2 + H^2
D^2 = 70^2 + 35^2 + 50^2
D^2 = 4900 + 1225 + 2500
D^2 = 8625
Taking the square root of both sides gives us:
D ≈ √8625
D ≈ 92.9 cm
Therefore, the length of the ramp needed to fit diagonally in the cage is approximately 92.9 cm.
To find the length of the ramp, we need to use the Pythagorean theorem to find the length of the diagonal of the rectangular prism.
First, we find the diagonal of the base of the rectangular prism using the Pythagorean theorem:
diagonal = √(length^2 + width^2)
diagonal = √(70^2 + 35^2)
diagonal = √(4900 + 1225)
diagonal = √6125
diagonal ≈ 78.2 cm
Next, we find the diagonal height of the rectangular prism:
diagonal height = √(diagonal^2 + height^2)
diagonal height = √(78.2^2 + 50^2)
diagonal height = √(6102.25 + 2500)
diagonal height = √(8602.25)
diagonal height ≈ 92.8 cm
Therefore, the ramp needs to be approximately 92.8 cm long.
To find the length of the ramp needed to fit diagonally in the cage, we can use 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.
In this case, we can consider the diagonal of the base of the cage (which is one side of the right triangle) and the height of the cage (which is another side of the right triangle). The missing side will be the length of the ramp.
Now, let's calculate the length of the ramp step-by-step:
1. Find the length of the diagonal of the base of the cage:
In a rectangular prism, the diagonal of the base can be found using the formula:
diagonal = √(length² + width²)
Given that the length of the cage is 70 cm and the width is 35 cm, we can calculate the diagonal of the base as:
diagonal = √(70² + 35²)
diagonal ≈ √(4900 + 1225)
diagonal ≈ √(6125)
diagonal ≈ 78.26 cm
2. Calculate the length of the ramp using the diagonal and the height of the cage:
Using the Pythagorean theorem, we have:
length of ramp = √(diagonal² + height²)
length of ramp ≈ √(78.26² + 50²)
length of ramp ≈ √(6121.2676 + 2500)
length of ramp ≈ √(8621.2676)
length of ramp ≈ 92.92 cm (rounded to the nearest tenth)
So, the length of the ramp needs to be approximately 92.9 cm to fit diagonally in the cage.