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, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
In this case, the ramp will form a right triangle with the height and length of the cage. So the length of the ramp, which is the hypotenuse, can be found using the formula:
ramp_length^2 = height^2 + length^2
Substituting the given values:
ramp_length^2 = 50^2 + 70^2
ramp_length^2 = 2500 + 4900
ramp_length^2 = 7400
Taking the square root of both sides:
ramp_length = √7400
ramp_length ≈ 86 cm
Therefore, the ramp needs to be approximately 86 cm long to fit diagonally in the cage.
To find the length of the ramp needed to fit diagonally in the cage, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square 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 cage can be considered as a right rectangular prism with a length of 70 cm, a width of 35 cm, and a height of 50 cm. We want to find the length of the ramp, which will be the hypotenuse of a right triangle formed by the length, width, and height of the prism.
Using the Pythagorean theorem, the length of the ramp (hypotenuse) is given by:
diagonal length = √(length^2 + width^2 + height^2)
Substituting the values:
diagonal length = √(70^2 + 35^2 + 50^2)
= √(4900 + 1225 + 2500)
= √(8625)
≈ 92.9 cm
Therefore, the ramp should be approximately 92.9 cm long to fit diagonally in the cage, rounded to the nearest tenth.
To find the length of the ramp needed to fit diagonally in the cage, we can use the Pythagorean theorem which states that the square of the hypotenuse (the longest side) equals the sum of the squares of the other two sides in a right triangle.
In this case, the length, width, and height of the cage form a right triangle. The length and width are the two sides of the base, and the height is the other side (the vertical height).
Using the Pythagorean theorem, we can calculate the length of the ramp:
Length^2 = Length of base^2 + Height^2
Length^2 = (70 cm)^2 + (50 cm)^2
Length^2 = 4900 cm^2 + 2500 cm^2
Length^2 = 7400 cm^2
To find the length, we take the square root of both sides:
Length = √(7400 cm^2)
Calculating this, we get:
Length ≈ 86 cm
Therefore, the ramp needs to be approximately 86 cm long to fit diagonally in the cage.