Question

1. △lmn~△pqr (find qr and pr)

qr = ____________ pr = ____________

Explanation:

Step1: Set up proportion for corresponding sides

Since $\triangle LMN\sim\triangle PQR$, the ratios of corresponding sides are equal. Let's set up the proportion for sides $MN$ and $QR$, and $LN$ and $PR$. The ratio of corresponding sides is $\frac{MN}{QR}=\frac{LN}{PR}=\frac{LM}{PQ}$. We know that $LM = 9$, $MN=15$, $LN = 21$ and $PQ = 12$. First, find the scale - factor using $\frac{LM}{PQ}=\frac{9}{12}=\frac{3}{4}$.

Step2: Find $QR$

We have the proportion $\frac{MN}{QR}=\frac{LM}{PQ}$. Substituting the known values, $\frac{15}{QR}=\frac{9}{12}$. Cross - multiply: $9\times QR=15\times12$. Then $QR=\frac{15\times12}{9}=\frac{180}{9} = 20$.

Step3: Find $PR$

We use the proportion $\frac{LN}{PR}=\frac{LM}{PQ}$. Substituting the values, $\frac{21}{PR}=\frac{9}{12}$. Cross - multiply: $9\times PR=21\times12$. Then $PR=\frac{21\times12}{9}=\frac{252}{9}=28$.

Answer:

$QR = 20$, $PR = 28$