Question

1. if the length of a rectangle is increased by 25% and the width is decreased by 10%, the area of the resulting rectangle is larger than the area of the original rectangle by what percent?

a. 2.5%
b. 12.5%
c. 15%
d. 22.5%
e. 35%

Explanation:

Step1: Let the original length and width

Let the original length be \(l\) and the original width be \(w\). The original area \(A = lw\).

Step2: Calculate the new length and width

The new length \(l_{new}=(1 + 0.25)l=1.25l\). The new width \(w_{new}=(1 - 0.10)w = 0.9w\).

Step3: Calculate the new area

The new area \(A_{new}=l_{new}\times w_{new}=1.25l\times0.9w\).

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Step4: Calculate the percentage increase

The percentage increase \(P=\frac{A_{new}-A}{A}\times100\%\). Substitute \(A = lw\) and \(A_{new}=1.125lw\) into the formula.

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Answer:

B. \(12.5\%\)