Question

a rectangle has an area of 30 square meter and a perimeter of 34 meters. what are the dimensions of rectangle?

Answer 1

$A=lw$
$P=2l+2w$

$30=lw$
$34=2l+2w$

$30=lw$ --> $w= \frac{30}{l}$

$34=2l+2( \frac{30}{l}) \\ 34=2l+ \frac{60}{l} \\ 34l=2l^2+60 \\ 2l^2-34l+60=0 \\ 2(l-2)(l-15)=0 \\ l=2, 15$

$30=(2)w$
$15=w$

$30=(15)w$
$2=w$

The dimensions can either be 15 x 2 or 2 x 15.