Question

The ratio of side lengths of square A to square B is $2:3$. The perimeter of square A is $16$ inches. What is the area of square B?

Answer 1

Step 1: Find the perimeter of square B

Given,

Ratio of side lengths of square A to square B is $2:3$.

Perimeter of square A is $16\mathrm{inches}$.

Since, we know that when two figures are similar then

$\Rightarrow \frac{PerimeterofsquareA}{PerimeterofsquareB}=\frac{SidelengthofsquareA}{SidelengthofsquareB}$

Using the criteria for similar figures.

$$\begin{gathered} \Rightarrow \frac{16}{PerimeterofsquareB}=\frac{2}{3} \\ \Rightarrow PerimeterofsquareB=\frac{16\times 3}{2}=24\mathrm{inches} \end{gathered}$$

Step 2: Find the side length of perimeter B

Now, we know perimeter of square = $4\times sidelength$

So,

$$\begin{gathered} \Rightarrow 4\times sidelength=24 \\ \Rightarrow sidelength=6\mathrm{inches} \end{gathered}$$

Step 3: Find the area of square B

Also, we know that area of square = ${(sidelength)}^2$.

So, area of square B = $6^2=36\mathrm{sq}.\mathrm{inches}$.

Hence, the area of square B is $36\mathrm{sq}.\mathrm{inches}$.