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
92.9 cm
92.9 cm
116.3 cm
116.3 cm
78.6 cm
78.6 cm
To find the length of the ramp, we need to calculate the length of the diagonal of the rectangular prism, which represents the hypotenuse of a right triangle formed by the length, width, and height.
Using the Pythagorean theorem, we have:
Diagonal^2 = length^2 + width^2 + height^2
Diagonal^2 = 70^2 + 35^2 + 50^2
Diagonal^2 = 4900 + 1225 + 2500
Diagonal^2 = 8625
Taking the square root of both sides, we get:
Diagonal = √8625
Diagonal ≈ 92.9 cm
Therefore, the ramp needs to be approximately 92.9 cm long.
To find the length of the ramp needed to fit diagonally in the cage, we can use the Pythagorean theorem. The equation for the Pythagorean theorem is a^2 + b^2 = c^2, where a and b are the lengths of the sides of a right triangle, and c is the length of the hypotenuse (the diagonal in this case).
In the given rectangular prism cage, the length is 70 cm, the width is 35 cm, and the height is 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 cage.
Let's label the length as a, the width as b, and the height as c. We can see that the length (a) and the width (b) of the cage form the two sides of a right triangle, and the ramp (c) is the hypotenuse.
Using the Pythagorean theorem, we can substitute the given values into the equation:
a^2 + b^2 = c^2
70^2 + 35^2 = c^2
4900 + 1225 = c^2
6125 = c^2
To find the length of the ramp (c), we need to take the square root of 6125:
c ≈ √6125 = 78.6 cm
Therefore, the length of the ramp needed to fit diagonally in the cage is approximately 78.6 cm, 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 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 length, width, and height of the cage form a right triangle. The ramp will be the hypotenuse.
The formula for the length of the hypotenuse (ramp) is:
√(length^2 + width^2 + height^2)
Plugging in the given values:
√(70^2 + 35^2 + 50^2) = √(4900 + 1225 + 2500) = √(8625) ≈ 92.9 cm
Therefore, the ramp needs to be approximately 92.9 cm long to fit diagonally in the cage.