Question

find x of QR? quadrilateral JKLM & PQRS are similar

Answer 1

x=3.2

Explanation

As the figures are similar we can make a proporiton

so

Step 1

let

$\text{ratio}=\frac{longest\text{ side}}{\text{smallest side}}$

hence

for figure JKLM

$\begin{gathered} \text{ratio}_1=\frac{JK}{LK} \\ \text{ratio}_1=\frac{7}{2} \end{gathered}$

for figure PQRS

$\begin{gathered} ratio_2=\frac{PQ}{RQ} \\ ratio_2=\frac{11.2}{x} \end{gathered}$

the ratio is the same, so the proportion is

$\text{ratio}_1=ratio_2$

replace

$\begin{gathered} \text{ratio}_1=ratio_2 \\ \frac{7}{2}=\frac{11.2}{x} \end{gathered}$

Step 2

solve for x

$\begin{gathered} \frac{7}{2}=\frac{11.2}{x} \\ \text{cross multiply } \\ 7\cdot x=2\cdot11.2 \\ 7x=22.4 \\ \text{divide both sides by 7} \\ \frac{7x}{7}=\frac{22.4}{7} \\ x=3.2 \end{gathered}$

therefore, the answer is

x=3.2

I hope this helps you