Question

1. if δklj ~ δvwu, find the value of x. diagram: top triangle k-l-j with side kl=25, kj=4x−23; bottom triangle v-w-u with side vw=20, vu=2x+2, angles at k and v marked congruent

Explanation:

Step1: Identify corresponding sides

Since \(\triangle KLJ \sim \triangle VWU\), their corresponding sides are proportional. So, \(\frac{KL}{VW}=\frac{KJ}{VU}\). Given \(KL = 25\), \(VW = 20\), \(KJ = 4x - 23\), \(VU = 2x + 2\).

Step2: Set up proportion equation

\(\frac{25}{20}=\frac{4x - 23}{2x + 2}\)

Step3: Cross - multiply

\(25(2x + 2)=20(4x - 23)\)
\(50x + 50 = 80x - 460\)

Step4: Solve for x

Subtract \(50x\) from both sides: \(50 = 30x - 460\)
Add 460 to both sides: \(510 = 30x\)
Divide by 30: \(x=\frac{510}{30}=17\)

Answer:

\(x = 17\)