Question

The width of Marie's bed is 40 inches and the distance between opposite corners is 85 inches. What is the length of Marie's bed?

Answer 1

To find the length of Marie's bed, the Pythagorean theorem was applied with the width (40 inches) and the diagonal (85 inches). The length calculated is 75 inches.

Step-by-step explanation:

The question asks us to determine the length of Marie's bed given the width and the distance between opposite corners. Since a bed forms a rectangle, we can apply the Pythagorean theorem because the distance between opposite corners represents the diagonal. The Pythagorean theorem states that in a right-angled 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): a2 + b2 = c2. Here, the width of the bed (40 inches) would be one side (a), the diagonal (85 inches) would be the hypotenuse (c), and we need to find the length (b).

Let's solve for b using the following steps:

1. Write down the Pythagorean theorem: a2 + b2 = c2.
2. Plug in the known values: 402 + b2 = 852.
3. Calculate 402 (which is 1600) and 852 (which is 7225).
4. Subtract 1600 from 7225, which gives us b2 = 5625.
5. Find the square root of 5625 to get the value of b, which is 75.

Thus, the length of Marie's bed is 75 inches.