Question

the length of a rectangle is 4in more than its width, and its perimeter is 34in find the length and width of the rectangle ​

Answer 1

Let $l$ and $w$ be, respectively, the length and the width of the rectangle.

If the length is 4 inches more than the width, we have

$l = w+4$

Moreover, the perimeter of a rectangle is given by

$2(l+w)$

And we can substitute $l=w+4$ to get

$2(w+4+w)=2(2w+4)=4w+8$

We know that the perimeter is 34 inches:

$4w+8=34 \iff 4w = 26 \iff w = \dfrac{26}{4}=6.5$

Which implies

$l=w+4=6.5+4=10.5$