# A small plane is flying a banner in the shape of a rectangle. The area of the banner is 144 square feet. The width of the banner is 1/4 the length of the banner. What are the dimensions of the banner?

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#### Explanation

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Tony B Share
Mar 11, 2016

Width is 6; Length is 24

#### Explanation:

Key points:

Rectangle shape

Area $\to 144 \text{ } f {t}^{2}$

Width = $\frac{\text{length}}{4}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let the area be $A = 144$
Let the width be $W$
Let the length be $L$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~
Known: $A = W \times L = 144$...........................(1)

Given: $W = \frac{L}{4}$.............................(2)

$\textcolor{b l u e}{\text{To determine the value of L}}$

Substitute (2) into (1) giving

$\frac{L}{4} \times L = 144$

$\implies {L}^{2} / 4 = 144$

Multiply both sides by 4

$\frac{4}{4} \times {L}^{2} = 144 \times 4$

${L}^{2} = 576$

Taking the square root of each side

$\textcolor{b l u e}{L = \sqrt{576} = 24}$
'~~~~~~~~~~~~~~~~~~~~~~~

$\textcolor{b l u e}{\text{To determine the value of W}}$

$W \times L = 144$

But L=24 so we have

$24 W = 144$

Divide both sides by 24

$\frac{24}{24} \times W = \frac{144}{24}$

$\textcolor{b l u e}{W = 6}$

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