Question

$\triangle ijk \sim \triangle hfg$. find $ik$ and $ij$.

Explanation:

Step1: Set up the proportion for similar triangles

Since \(\triangle IJK\sim\triangle HFG\), the ratios of corresponding sides are equal.
For \(IK\) and \(HG\), \(IJ\) and \(FH\), \(JK\) and \(FG\).
We have \(\frac{IK}{HG}=\frac{JK}{FG}\) and \(\frac{IJ}{FH}=\frac{JK}{FG}\)

Step2: Find \(IK\)

We know \(JK = 6\), \(FG=30\), \(HG = 35\)
Using \(\frac{IK}{HG}=\frac{JK}{FG}\), substitute the values: \(\frac{IK}{35}=\frac{6}{30}\)
Cross - multiply: \(30\times IK=35\times6\)
\(IK=\frac{35\times6}{30}=\frac{210}{30} = 7\)

Step3: Find \(IJ\)

We know \(FH = 50\), \(JK = 6\), \(FG = 30\)
Using \(\frac{IJ}{FH}=\frac{JK}{FG}\), substitute the values: \(\frac{IJ}{50}=\frac{6}{30}\)
Cross - multiply: \(30\times IJ=50\times6\)
\(IJ=\frac{50\times6}{30}=\frac{300}{30}=10\)

Answer:

\(IK = 7\) and \(IJ = 10\)