Question

If JK = 28, JL = 20, KL = 13, and ML = 22, calculate NL. Image not set to scale.

Answer 1

NL = 440 /13 or 33.85 (to two decimals)

Explanation:

Consider triangles JKL and NML

angle JLK = angle NLM vertical angles

angle KJL = angle MNL given

Therefore triangles JKL and NML are similar

By proportion of corresponding sides of similar triangles,

NL / JL = LM / LK

Substitute given values

NL / 20 = 22 / 13

solve for NL

NL = 20*22 / 13 = 440 /13 or 33.85 (to two decimals)

Answer 2

`\huge \boxed{33.85}`

Explanation:

JL is similar to NL. KL is similar to ML.

We can use ratios to solve.

JL/KL = NL/ML

Let the length of NL be x.

20/13 = x/22

Cross multiply.

13 × x = 22 × 20

13x = 440

Divide both sides by 13.

(13x)/13 =440/13

x = 440/13 = 33.846154...