Question

1. a rectangle has the dimensions shown. the length of each side is quadrupled. how many times larger is the new area when compared to the original? (numerical value only)

Explanation:

Step1: Calculate original area

The original rectangle has length $l = 6$ and width $w = 4$. The area formula for a rectangle is $A = l\times w$. So the original area $A_{1}=6\times4 = 24$.

Step2: Calculate new - side lengths

Each side is quadrupled. The new length $l_{2}=6\times4 = 24$ and the new width $w_{2}=4\times4 = 16$.

Step3: Calculate new area

Using the area formula $A = l\times w$, the new area $A_{2}=l_{2}\times w_{2}=24\times16 = 384$.

Step4: Find the ratio of new area to original area

The ratio $\frac{A_{2}}{A_{1}}=\frac{384}{24}=16$.

Answer:

16