Question

1. if δnml ~ δsrl, find the value of x.

(diagram with points m, n, l, s, r; ml = 28, rl = 24, nl = 3x - 1, sl = x + 7)

Explanation:

Step1: Use Similar Triangles Proportion

Since \(\triangle NML \sim \triangle SRL\), the corresponding sides are proportional. So \(\frac{ML}{RL}=\frac{NL}{SL}\).
Given \(ML = 28\), \(RL = 24\), \(NL = 3x - 1\), \(SL = x + 7\), we have \(\frac{28}{24}=\frac{3x - 1}{x + 7}\).

Step2: Cross - Multiply

Cross - multiply the proportion: \(28(x + 7)=24(3x - 1)\).
Expand both sides: \(28x+196 = 72x-24\).

Step3: Solve for x

Subtract \(28x\) from both sides: \(196=72x - 28x-24\).
Simplify: \(196 = 44x-24\).
Add 24 to both sides: \(196 + 24=44x\).
\(220 = 44x\).
Divide both sides by 44: \(x=\frac{220}{44}=5\).

Answer:

\(x = 5\)