Question

triangle nop is similar to triangle qrs. find the measure of side sq. figures are not drawn to scale.

Explanation:

Step1: Set up proportion

Since the triangles are similar, the ratios of corresponding sides are equal. Let the side corresponding to side $SQ$ in $\triangle NOP$ be side $NP$. So we have the proportion $\frac{SQ}{NP}=\frac{QR}{NO}$. Here we assume the sides are in proportion and we know $NP = 2$, and let's assume the ratio of similarity is based on the pair of known - corresponding sides. Let's assume the side $QR$ corresponds to side $NO$. We can set up the proportion using the ratio of the known non - corresponding sides. If we assume the ratio of the sides of the two similar triangles is the same for all corresponding sides, we have $\frac{SQ}{2}=\frac{16.8}{3}$.

Step2: Solve for $SQ$

Cross - multiply the proportion $\frac{SQ}{2}=\frac{16.8}{3}$ to get $3\times SQ=2\times16.8$. Then $3SQ = 33.6$. Divide both sides by 3: $SQ=\frac{33.6}{3}=11.2$.

Answer:

$11.2$