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 10th
To find the length of the ramp needed, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In this case, the length of the ramp would be the hypotenuse of a right triangle where the base and height are the dimensions of the cage.
Let's define:
- a = length of the cage (70 cm)
- b = width of the cage (35 cm)
- c = length of the ramp
So, the Pythagorean theorem can be expressed as:
c^2 = a^2 + b^2
c^2 = 70^2 + 35^2
c^2 = 4900 + 1225
c^2 = 6125
Now, we can find the square root of 6125 to get the length of the ramp:
c = sqrt(6125)
c ≈ 78.3 cm
Therefore, the ramp needs to be approximately 78.3 cm long to fit diagonally in the cage.