Question

The perimeter of a rectangle is 54 inches and its area is 182 square inches. How do you find the length and width of the rectangle?

Answer 1

The sides of the rectangle are 13 and 14 inches.

Explanation:

`2a+2b=54`
`axxb=182`

`a=182/b`

`2xx(182/b)+2b=54`

`364/b+2b=54`

Multiplying by "b":

`364+2b^2=54b`

`2b^2-54b+364=0`

Solving the quadratic equation:

`b_1 = 14`
`a_1=182/14=13`

`b_2=13`
`a_2=182/13=14`

The sides of the rectangle are 13 and 14 inches.