Question

A square and a rectangle have the same perimeter. The square has an area of 81 sq. inches and the rectangle has a width of 5 in. What is the area of the rectangle?

Answer 1

Area of rectangle =
`\mbox{\large \boxed{\textrm{65 sq. inches}}}`

Explanation:

Let square side =
`a`

Area of square
`A = a^2`

Given
`A = 81` and equating it to
`a^2`

`a^2`
`= 81\;in^2`

`a = √(81) = 9\;in`

Perimeter of square =
`4a = 4\cdot 9 = 36 \;in`

If
`l` = length of the rectangle and
`w` = width

Perimeter P of rectangle =
`2(l + w)\\`

Given perimeter of rectangle = perimeter of square we get

`2(l + w) = 36\\\\l + w = 36/2\\\\l + w = 18`

Given

`w = 5\\\\l + 5 = 18\\\\l = 18 - 5 = 13\\\\`

`\\\\\textrm{Area of rectangle } = l * w\\\\= 13 * 5 \\\\= 65 \;sq.\;inches`