Question

question 12
note: figure not drawn to scale.
△qpr is similar to △str. the lengths represented by st, qp, pr, and qr in the figure are 14, 15, 20, and 25, respectively. what is the length of sr?
a) 350/15
b) 350/20
c) 210/20
d) 210/25

Explanation:

Step1: Recall similar - triangles property

For similar right - triangles $\triangle QPR$ and $\triangle STR$, the ratios of corresponding sides are equal. That is, $\frac{QP}{ST}=\frac{PR}{TR}=\frac{QR}{SR}$.

Step2: Set up the proportion for unknown side

We know that $\frac{QP}{ST}=\frac{QR}{SR}$. Given $QP = 15$, $ST = 14$, and $QR = 25$. Substitute these values into the proportion: $\frac{15}{14}=\frac{25}{SR}$.

Step3: Cross - multiply to solve for SR

Cross - multiplying gives us $15\times SR=14\times25$. Then $SR=\frac{14\times25}{15}=\frac{350}{15}$.

Answer:

A. $\frac{350}{15}$