Question

The area of a rectangle is 640 $m^2$. Taking in length as x m; find, in terms of x, the width of the rectangle. If the perimeter of the rectangle is 104 m; find its dimensions.

Answer 1

Area of rectangle$=640m^2$

$l\times b=640$ ,length = x

$x\times b=640----\left(i\right)$

Perimeter = 104

$2(x+b)=104$

$x+b=52$

$\frac{640}{b}+b=52$ by (i)

$640+b^2=52b$

$b^2-52b+640=0$

$b^2-32b-20b+640=0$

$b(b-32)-20(b-32)=0$

$(b-32)(b-20)=0$

$b=32,20$

$x=20,32$