Question

in the diagram below, $\triangle ghi \sim \triangle jhk$. find $v$.

diagram showing two right triangles, $\triangle ghi$ with legs $v$ and 15 m, and $\triangle jhk$ with leg 60 m and hypotenuse 68 m, sharing a common right angle at $h$ on segment $gj$

write your answer as a whole number or a decimal. do not round.
$v = \square$ meters

Explanation:

Step1: Identify corresponding sides

Since $\triangle GHI \sim \triangle JHK$, the ratios of corresponding sides are equal. The sides $GI$ (length $v$) and $JK$ (length $68$ m) are corresponding, and sides $GH$ (length $15$ m) and $JH$ (length $60$ m) are corresponding.

Step2: Set up proportion

Using the similarity of triangles, we set up the proportion $\frac{GI}{JK}=\frac{GH}{JH}$. Substituting the known values, we get $\frac{v}{68}=\frac{15}{60}$.

Step3: Solve for \( v \)

Cross - multiply: $60v = 15\times68$. Calculate $15\times68 = 1020$. Then, $v=\frac{1020}{60}=17$.

Answer:

17