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 :} \\ (FG)/(IJ)=(GH)/(JK)=(HF)/(KI) \end{gathered}`

Substiute the vale :

`\begin{gathered} (FG)/(IJ)=(GH)/(JK)=(HF)/(KI) \\ (5)/(23)=(3.5)/(JK)=(HF)/(KI) \end{gathered}`

We need to find the length of JK , Simplify the

Susbstitutw thw vales and simlify :

`\begin{gathered} (FG)/(IJ)=(GH)/(JK)=(HF)/(KI) \\ (5)/(23)=(3.5)/(J) \\ 5J=\text{ 2.5}*2.5x \\ J=\frac{2.5\text{ }*2.4}{2} \\ J=0.625 \end{gathered}`