Question

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Our school flag is a rectangle. We are changing to a new rectangular flag design. The length of the new flag is 20% greater than the length of the old flag, and the width of the new flag is 10% less than the width of the old flag, The old school flag is 25 square feet. What is the area of the new flag?

Answer 1

Answer: Hence the answer is 27 square feet.

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Answer 2

Answer:

27 square feet

Step-by-step explanation:

Define the variables:

• Let w be the width of the old flag.
• Let l be the length of the old flag.

To increase a number by a certain percent, divide the percent by 100, add it to 1, then multiply the original number by this number.

If the length of the new flag is 20% greater than the length of the old flag:

$\implies \textsf{Length}=\left(1+\dfrac{20}{100}\right) \timesl \times l=1.2l$

To decrease a number by a certain percent, divide the percent by 100, subtract it from 1, then multiply the original number by this number.

If the width of the new flag is 10% less than the width of the old flag:

$\implies \textsf{Width}=\left(1-\dfrac{10}{100}\right) \times w =0.9w$

$\boxed{\textsf{Area of a rectangle}=\sf width \times length}$

Therefore, given the area of the old flag is 25 ft²:

$\implies wl=25$

To find the area of the new flag, substitute the expressions for width, length and wl into the formula for area of a rectangle:

$\begin{aligned}\textsf{Area of new flag}&=\sf width \times length\\&=0.9w \times 1.2l\\&=0.9 \times 1.2 \times wl\\&=1.08 \times 25\\&=27\sf \;\; ft^2\end{aligned}$

Therefore, the area of the new flag is 27 square feet.