Question

1. if δstu ~ δplm, find the value of x.

(image of two triangles: δstu with sides st = x + 1, tu = 2x - 3; δplm with sides pl = 72, lm = 99, pm = 70)

Explanation:

Step1: Use the property of similar triangles

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

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:
\(99 + 216=144x-99x\)
\(315 = 45x\)
Divide both sides by \(45\): \(x=\frac{315}{45}=7\)

Answer:

\(x = 7\)