Question

Triangle FGH is similar to triangle IJK. Find the measure of side JK. Round your answer to the nearest tenth if necessary.

Answer 1

The given set of traimgels FGH and IJK :

Triangles FGH and IJK are similar

From the properties of similar triangle

The ratio of the length of corrsponding sides of similar triangle are always equal

$\begin{gathered} \text{ For }\Delta FGH\text{ }\approx\Delta IJK \\ \text{ Corresponing sides :} \\ \frac{FG}{IJ}=\frac{GH}{JK}=\frac{HF}{KI} \end{gathered}$

Substiute the vale :

$\begin{gathered} \frac{FG}{IJ}=\frac{GH}{JK}=\frac{HF}{KI} \\ \frac{5}{23}=\frac{3.5}{JK}=\frac{HF}{KI} \end{gathered}$

We need to find the length of JK , Simplify the

Susbstitutw thw vales and simlify :

$\begin{gathered} \frac{FG}{IJ}=\frac{GH}{JK}=\frac{HF}{KI} \\ \frac{5}{23}=\frac{3.5}{J} \\ 5J=\text{ 2.5}\times2.5x \\ J=\frac{2.5\text{ }\times2.4}{2} \\ J=0.625 \end{gathered}$