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)
To find the length of the ramp, we can use the Pythagorean theorem.
The diagonal of the cage can be found by finding the diagonal of the base, which is a rectangle with length 70 cm and width 35 cm, and the height of the cage. The diagonal D can be found using the formula
D = √(L^2 + W^2 + H^2),
where L is the length, W is the width, and H is the height of the prism.
Substituting the given values, we get
D = √(70^2 + 35^2 + 50^2)
= √(4900 + 1225 + 2500)
= √(8625)
≈ 92.9 cm
Therefore, the ramp needs to be approximately 92.9 cm long, rounded to the nearest tenth.
To determine the length of the ramp needed to fit diagonally in the rectangular prism cage, we can use the Pythagorean theorem.
The Pythagorean theorem 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 of the ramp is the hypotenuse, and the dimensions of the cage represent the other two sides of the right triangle.
Let's calculate the length of the ramp:
Length of the ramp^2 = Length^2 + Width^2 + Height^2
Length of the ramp^2 = 70^2 + 35^2 + 50^2
Length of the ramp^2 = 4900 + 1225 + 2500
Length of the ramp^2 = 8625
To find the length of the ramp, we take the square root of both sides:
Length of the ramp = √8625
Length of the ramp ≈ 92.8 cm
Therefore, the ramp needs to be approximately 92.8 cm long to fit diagonally in the cage.
To find the length of the ramp, we can use the Pythagorean theorem because we have a right-angled triangle formed by the length, width, and height of the cage. The ramp will be the hypotenuse of this triangle.
The formula for the Pythagorean theorem is:
c^2 = a^2 + b^2
Where c is the length of the hypotenuse (ramp) and a and b are the lengths of the other two sides.
In this case, we need to find the length of the ramp, so let's identify the other two sides:
a = length of the cage = 70 cm
b = width of the cage = 35 cm
Now, we can substitute these values into the formula:
c^2 = 70^2 + 35^2
c^2 = 4900 + 1225
c^2 = 6125
To find the length of the ramp, we take the square root of both sides:
c = √6125
Calculating this gives us:
c ≈ 78.2 cm
Therefore, the length of the ramp needs to be approximately 78.2 cm to fit diagonally in the cage.