Question

△ dns ~△ arh
what is the value of x?
enter your answer in the box.
□ units

Explanation:

Step1: Identify corresponding sides

Since $\triangle DNS \sim \triangle ARH$, the corresponding sides are proportional. So, $\frac{DN}{AR} = \frac{DS}{AH}$.

Step2: Substitute known values

We know $DN = 72$, $AR = 21.6$, and $DS = 110$. Let $AH = x$. Then we have the proportion $\frac{72}{21.6} = \frac{110}{x}$.

Step3: Solve for x

First, simplify $\frac{72}{21.6} = \frac{720}{216} = \frac{10}{3}$. So, $\frac{10}{3} = \frac{110}{x}$. Cross - multiply: $10x = 3\times110$. Then $10x = 330$. Divide both sides by 10: $x=\frac{330}{10}=33$.

Answer:

33