Question

1. if \\( \triangle stu \sim \triangle plm \\), find the value of \\( x \\).

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle STU\sim\triangle PLM\), the ratios of corresponding sides are equal.
\(\frac{ST}{PL}=\frac{TU}{LM}\)
Here, \(ST = x + 1\), \(PL=72\), \(TU = 2x-3\), \(LM = 99\)
So, \(\frac{x + 1}{72}=\frac{2x-3}{99}\)

Step2: Cross - multiply

Cross - multiplying gives \(99(x + 1)=72(2x-3)\)
Expand both sides: \(99x+99 = 144x-216\)

Step3: Solve for \(x\)

Move the \(x\) terms to one side and constants to the other side:
\(144x-99x=99 + 216\)
\(45x=315\)
Divide both sides by \(45\): \(x=\frac{315}{45}=7\)

Answer:

\(7\)