Question

by decreasing each dimension by 2 units, the area of a rectangle decreased from 48 square feet (on the left) to 24 square feet (on the right). find the percent decrease in area.
the percent decrease in area is %.

Explanation:

Step1: Calculate the original area

The original area \(A_1 = 48\) square feet.

Step2: Calculate the new area

The new area \(A_2=24\) square feet.

Step3: Use the percentage - decrease formula

The percentage - decrease formula is \(\text{Percentage decrease}=\frac{A_1 - A_2}{A_1}\times100\%\).
Substitute \(A_1 = 48\) and \(A_2 = 24\) into the formula: \(\frac{48 - 24}{48}\times100\%=\frac{24}{48}\times100\%\).
Simplify \(\frac{24}{48}=\frac{1}{2}\), and \(\frac{1}{2}\times100\% = 50\%\).

Answer:

\(50\)