Question

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar.
a rectangle is 12 feet long and 5 feet wide. if the length of the rectangle is increased by 25% and the width is decreased by 20%, what is the change in the area of the rectangle?
the change in the area of the rectangle is square feet.

Explanation:

Step1: Calculate the original area

The formula for the area of a rectangle is \(A = l\times w\). Given \(l = 12\) feet and \(w = 5\) feet.
\(A_{original}=12\times5 = 60\) square feet.

Step2: Calculate the new length

The length is increased by \(25\%\). The new - length \(l_{new}=l\times(1 + 25\%)\). Since \(25\%=\frac{25}{100}=0.25\), then \(l_{new}=12\times(1 + 0.25)=12\times1.25 = 15\) feet.

Step3: Calculate the new width

The width is decreased by \(20\%\). The new - width \(w_{new}=w\times(1 - 20\%)\). Since \(20\%=\frac{20}{100}=0.2\), then \(w_{new}=5\times(1 - 0.2)=5\times0.8 = 4\) feet.

Step4: Calculate the new area

Using the area formula \(A = l\times w\) with \(l_{new}=15\) feet and \(w_{new}=4\) feet.
\(A_{new}=15\times4=60\) square feet.

Step5: Calculate the change in area

The change in area \(\Delta A=A_{new}-A_{original}\).
\(\Delta A = 60 - 60=0\)

Answer:

\(0\)