Question

1. find the value of x:

△klm ~ △gfe

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle KLM\sim\triangle GFE\), the ratios of corresponding sides are equal. That is \(\frac{KL}{GF}=\frac{LM}{FE}\).
We know \(KL = 24\), \(GF=16\), \(LM = 4x - 5\), and \(FE = 18\). So, \(\frac{24}{16}=\frac{4x - 5}{18}\).

Step2: Cross - multiply

Cross - multiplying gives \(24\times18=16\times(4x - 5)\).
First, calculate \(24\times18 = 432\) and \(16\times(4x - 5)=64x-80\). So, \(432=64x - 80\).

Step3: Solve for \(x\)

Add \(80\) to both sides: \(432 + 80=64x\), which simplifies to \(512 = 64x\).
Then divide both sides by \(64\): \(x=\frac{512}{64}\).

Answer:

\(x = 8\)