Question

Find the area of a rectangle having a perimeter of 182 yards and a width 20 yards shorter than twice its length


`l * w`

Answer 1

Let the length be
`l` in this equation.

We know that the perimeter of a rectangle is
`w2 + l2 = P`

Width is defined in terms of length, so we know
`w = l2 - 20`

We can substitute this value of w into the formula for perimeter to find the length.


`(l2 - 20)2 + l2 = 182`


`l4 - 40 + l2 = 182`


`l4 + l2 = 222`


`l6 = 222`


`l = 37`

So the length is 37. Now that we've found the length, we can go back to the Perimeter formula again and find width.


`w2 + (37)2 = 182`


`w2 + 74 = 182`


`w2 = 108`


`w = 54`

Width is 54. Now with both of these values found, we can calculate area with the formula
`l * w = A`


`37 * 54 = A`


`1998 = A`

So the area of the rectangle is 1998 yards^2.