Question

Find x of QR? quadrilateral JKLM & PQRS are similar

Answer 1

x=3.2

Step-by-step 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=(JK)/(LK) \\ \text{ratio}_1=(7)/(2) \end{gathered}`

for figure PQRS

`\begin{gathered} ratio_2=(PQ)/(RQ) \\ ratio_2=(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 \\ (7)/(2)=(11.2)/(x) \end{gathered}`

Step 2

solve for x

`\begin{gathered} (7)/(2)=(11.2)/(x) \\ \text{cross multiply } \\ 7\cdot x=2\cdot11.2 \\ 7x=22.4 \\ \text{divide both sides by 7} \\ (7x)/(7)=(22.4)/(7) \\ x=3.2 \end{gathered}`

therefore, the answer is

x=3.2

I hope this helps you