Question

if ( jk = 25 ), ( jl = 21 ), ( kl = 14 ), and ( ml = 20 ), calculate ( nl ). image not set to scale.

Explanation:

Step1: Use the similarity of triangles

Since \(\angle JKL=\angle NML\) (vertical angles) and \(\angle J=\angle M\) (given), \(\triangle JKL\sim\triangle NML\) by the AA (Angle - Angle) similarity criterion.

Step2: Set up the proportion

For similar triangles \(\triangle JKL\) and \(\triangle NML\), we have the proportion \(\frac{JK}{NM}=\frac{JL}{ML}=\frac{KL}{NL}\). Using \(\frac{JK}{NL}=\frac{JL}{ML}\), substitute \(JK = 25\), \(JL=21\), \(KL = 14\), and \(ML = 20\). Let \(NL=x\). Then \(\frac{25}{x}=\frac{21}{20}\).

Step3: Solve for \(x\)

Cross - multiply: \(21x=25\times20\). So \(21x = 500\), and \(x=\frac{500}{21}\approx23.81\).

Answer:

\(\frac{500}{21}\)