Question

a qpr is similar to △ str. the lengths represented by st, qp, pr, and qr in the figure are 17, 21, 28, 35 respectively. what is the length of sr? a. 21/595 b. 28/595 c. 28/357 d. 35/357 note : figure not drawn to scale

Explanation:

Step1: Identify corresponding sides

Since $\triangle QPR\sim\triangle STR$, the ratios of corresponding sides are equal. The corresponding sides are $\frac{QP}{ST}=\frac{PR}{TR}=\frac{QR}{SR}$. We know $QP = 21$, $ST = 17$, $PR=28$, $QR = 35$, and we want to find $SR$.

Step2: Set up proportion

Using the proportion $\frac{QR}{SR}=\frac{QP}{ST}$, we substitute the known values: $\frac{35}{SR}=\frac{21}{17}$.

Step3: Cross - multiply

Cross - multiplying gives us $21\times SR=35\times17$.

Step4: Solve for SR

$SR=\frac{35\times17}{21}=\frac{595}{21}$.

Answer:

a. $\frac{595}{21}$