# The length of a rectangle is four times the width. The area is 1444. How do you find the width and length?

Mar 25, 2018

$\text{width "=19," length } = 76$

#### Explanation:

$\text{let the width } = w$

$\Rightarrow \text{length "=4wlarrcolor(blue)"four times the width}$

• " area of rectangle "="length "xx"width"

$\Rightarrow \text{area } = 4 w \times w = 4 {w}^{2}$

$\text{now area } = 1444$

$\text{equating the expression and given value for area}$

$\Rightarrow 4 {w}^{2} = 1444$

$\text{divide both sides by 4}$

$\frac{\cancel{4} {w}^{2}}{\cancel{4}} = \frac{1444}{4}$

$\Rightarrow {w}^{2} = 361$

$\textcolor{b l u e}{\text{take the square root of both sides}}$

$\Rightarrow w = \pm \sqrt{361} \leftarrow \textcolor{b l u e}{\text{note plus or minus}}$

$\Rightarrow w = \pm 19$

$\text{but "w>0rArrw=19larrcolor(red)"width}$

$\text{and "4w=(4xx19)=76larrcolor(red)"length}$

Mar 25, 2018

$\text{width} = 19$, $\text{length} = 76$.

#### Explanation:

If we double the width and halve the length, then the rectangle will have the same area $1444$, but it will be a square with sides $\sqrt{1444} = 38$.

So the original length of the rectangle is $2 \cdot 38 = 76$ and width $\frac{38}{2} = 19$