# The length of a rectangle is 4 inches more than its width, and its perimeter is 34 inches. What is the length and width of the rectangle?

Mar 2, 2018

Length l = 10.5”, Width w = 6.5”

#### Explanation: Perimeter $P = 2 l + 2 w$

Given l =( w + 4)”, P = 34”

$\therefore 34 = 2 \left(w + 4\right) + 2 w$

$4 w + 8 = 34$

w = 26/4 = 6.5”

l = w + 4 = 6.5 + 4 = 10.5”

Mar 2, 2018

length is $10.5$ inches

width is $6.5$ inches

#### Explanation:

Let length be $l$
Let width be $w$
Let perimeter be $P$

First, we must construct an equation for these variables:

$l = w + 4$

$P = 34$

But, Perimeter of a rectangle $= l + w + l + w$

$= 2 l + 2 w$

So:

$34 = 2 l + 2 w$

But, since $l = w + 4$, we can substitute for $l$, having only the $w$ variable:

$34 = 2 \left(w + 4\right) + 2 w$

$34 = 2 w + 8 + 2 w$

$34 = 4 w + 8$

Solve for $w$:

$4 w = 34 - 8$

$4 w = 26$

$w = \frac{26}{4}$

$w = 6.5$ inches

Now, we can substitute $6.5$ for $w$ in the Perimeter Equation:

$34 = 2 l + 2 w$

becomes:

$34 = 2 l + 2 \cdot 6.5$

$34 = 2 l + 13$

Solve for $l$:

$2 l = 34 - 13$

$2 l = 21$

$l = \frac{21}{2}$

$l = 10.5$ inches

Thus, length is $10.5$ inches

Thus, width is $6.5$ inches