Chapter 7.3, Problem 7CYU

To determine

To identify: the similar triangle and find the value of the given length.

Answer to Problem 7CYU

  $\Delta QVS=\Delta RTS$ , $VS=20$ .

Explanation of Solution

Given:

The given length is $VS$

  

Calculation:

From the above triangle in the figure,

  $\begin{array}{l}\angle V=\angle T={90}^{\circ }\left\{given\right\}\\ \angle S=\angle S\left\{\text{common}\right\}\\ \text{therefore, by AA-aimilarity,}\\ \Delta QVS=\Delta RTS\end{array}$

Since, the triangles are similar, therefore the corresponds sides are proportional. Thus,

  $\begin{array}{l}\frac{QV}{RT}=\frac{VS}{TS}\\ \Rightarrow \frac{5}{3}=\frac{VS}{12}\left\{\text{substitutes these value}\right\}\\ \therefore VS=\frac{5\times 12}{3}=20\end{array}$ .

Hence, the similar triangle is $\Delta XYZ=\Delta JKL$ and find the value of the given length $VS=20$ .