Question

question
if the length of a rectangle is increased by 30% and the width of the same rectangle is decreased by 30%,
what is the effect on the area of the rectangle?
o it is increased by 60%.
o it is unchanged.
o it is decreased by 15%.
o it is decreased by 9%.

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 \(l_{new}=(1 + 0.3)l=1.3l\). The new width \(w_{new}=(1 - 0.3)w = 0.7w\).

Step3: Calculate the new area

The new area \(A_{new}=l_{new}\times w_{new}=1.3l\times0.7w\). Using the multiplication formula \(1.3\times0.7 = 0.91\), so \(A_{new}=0.91lw\).

Step4: Calculate the percentage change

The percentage change in area is \(\frac{A - A_{new}}{A}\times100\%=\frac{lw-0.91lw}{lw}\times 100\%=(1 - 0.91)\times100\% = 9\%\) decrease.

Answer:

It is decreased by 9%.