# A rectangular school banner has a length of 44 inches, a perimeter of 156 inches, and an area of 1496 square inches. The cheerleader make signs similar to the banner. The length of a sign is 11 inches. What is the perimeter and its area?

Jun 24, 2017

$\text{perimeter "=39" inches", "area "=93.5" sq inches}$

#### Explanation:

$\text{in similar figures the ratios of corresponding sides are equal}$

$\text{for similar rectangles the corresponding sides are the lengths}$
$\text{and widths}$

$\text{ratio of lengths (k ) } = \frac{11}{44} = \frac{1}{4}$

• "perimeter of banner "=2l+2w=156

$\text{where "l="length and " w=" width}$

$\Rightarrow w = \frac{1}{2} \left(156 - \left(2 \times 44\right)\right) = 34 \text{ inches}$

$\Rightarrow \text{width of model "=1/4xx34=8.5" inches}$

• " perimeter of model "=(2xx11)+(2xx8.5)

$\textcolor{w h i t e}{\times \times \times \times \times \times \times \times} = 39 \text{ inches}$

$\text{there are 2 possible approaches to calculating the}$
$\text{area of the model}$

• " area " =lw=11xx8.5=93.5" sq inches"

$\textcolor{red}{\text{OR}}$

$\text{area "=1496xx(1/4)^2=93.5" sq inches}$