# The length of rectangle is 5 more than the width. The perimeter is 22 feet. How do you find the length and width?

Apr 6, 2017

$W = \frac{11}{6} \text{ ft" = 1 " ft " 10 " inches" = 22 " inches}$
$L = 9 \text{ ft " 2 " inches" = 110 " inches}$

#### Explanation:

Given: $L = 5 W$, Perimeter $= 22 \text{ ft}$

Perimeter, $P = 2 L + 2 W$

$22 = 2 \left(5 W\right) + 2 W$

Distribute and solve for $W$:

$22 = 10 W + 2 W$
$22 = 12 W$

$W = \frac{22}{12} = \frac{11}{6} \text{ ft" = 1 " ft " 10 " inches" = 22 " inches}$

$L = 5 W = 5 \cdot \frac{11}{6} = \frac{55}{6} = 9 \text{ ft " 2 " inches" = 110 " inches}$

Apr 6, 2017

length: 8
width: 3

#### Explanation:

$a$=length;
$b$=width;

$a = b + 5$ --> length is 5 more than the width

$22 = 2 a + 2 b$ --> div all by 2
$11 = a + b$
$b = 11 - a$

$b = 11 - b - 5$
$2 b = 6$

$b = 3$
$a = b + 5 = 3 + 5 = 8$

$2 \cdot 8 + 2 \cdot 3 = 16 + 6 = 22$ --> CORRECT