Question

1. triangle nop is similar to triangle rst. find tr. round your answer to the nearest tenth if necessary. figures are not drawn to scale.

Explanation:

Step1: Set up proportion

Since $\triangle NOP\sim\triangle RST$, the ratios of corresponding - sides are equal. That is, $\frac{NP}{TR}=\frac{NO}{RS}$. We know that $NP = 10$, $NO = 7$, and $RS = 32$. Let $TR=x$. So the proportion is $\frac{10}{x}=\frac{7}{32}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{10}{x}=\frac{7}{32}$ gives us $7x=10\times32$.

Step3: Solve for x

First, calculate $10\times32 = 320$. Then, we have the equation $7x = 320$. Divide both sides of the equation by 7: $x=\frac{320}{7}\approx45.7$.

Answer:

$45.7$