Question

The area of a square is 20 cm^ 2. Its side length is enlarged by a scale factor of 4. What is the area of the new square?

Answer 1

The area of a square is 20 cm^ 2. Its side length is enlarged by a scale factor of 4. What is the area of the new square?

we know that

the area of a square is equal to

A=b^2

where

b is the length side

we have

A=20 cm^2

substitute

20=b^2

square root both sides

`\begin{gathered} b=\sqrt[]{20\text{ cm}} \\ b=2\sqrt[]{5\text{ cm}} \end{gathered}`

the side length is enlarged by a scale factor of 4

so

the new length side is equal to

`\begin{gathered} b=4(2\sqrt[]{5)} \\ b=8\sqrt[]{5\text{ cm}} \end{gathered}`

Find the new area

`\begin{gathered} A=(8\sqrt[]{5})^2 \\ A=320\text{ cm\textasciicircum{}2} \end{gathered}`

another way to find the area is multiply the original area by the scale factor squared

20

A=20(4^2)=320 cm^2