Question

triangle nop is similar to triangle qrs. find the measure of side sq. figures are not drawn to scale.
p
2
3
n
o
s
16.8
q
r

Explanation:

Step1: Identify corresponding sides

Since $\triangle NOP \sim \triangle QRS$, the ratio of corresponding sides is equal. Side $OP$ (length 3) corresponds to side $RS$ (length 16.8), and side $NP$ (length 2) corresponds to side $SQ$ (let's call its length $x$).

Step2: Set up proportion

The proportion of corresponding sides is $\frac{NP}{SQ} = \frac{OP}{RS}$. Substituting the known values: $\frac{2}{x} = \frac{3}{16.8}$.

Step3: Solve for $x$

Cross - multiply: $3x = 2\times16.8$. Then $3x = 33.6$. Divide both sides by 3: $x=\frac{33.6}{3}=11.2$.

Answer:

11.2