Given:

△EGH ~ △IKL, HF and LJ are medians. HE = 9, LI = 6, HF = x+2, and LJ = 2x−4

Find:

HF

The fact that the largest triangles are similar and that HF and LJ are medians, we know that triangle HFE and triangle LJI are congruent.
Similarity allows us to set up proportions of congruent sides.
(Write these fractions vertically and solve.
9/6 = (x + 2)/(2x - 4)

9(2x - 4) = 6(x + 2)
18x - 36 = 6x + 12
-6x. -6x
12x - 36 = 12
+36. +36
12x = 48
x = 4 ...... but WAIT! HF = x + 2 so 4 + 2 = 6

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raphealnwobi raphealnwobi · Answer 2 · 2022-03-28T11:45:47+02:00

The value of HF in the triangle EGH is 6 units.

What are similar triangles?

Two triangles are said to be similar if they have the same shape and the ratio of their corresponding sides are in the same proportion.

Triangle EGH is similar to triangle IKL, hence:

HE / IL = HF / LJ

HE = 9, LI = 6, HF = x+2, and LJ = 2x−4

substituting:

9 / 6 = (x + 2) / (2x - 4)

18x - 36 = 6x + 12

x = 4

HF = x + 2 = 4 + 2 = 6

The value of HF in the triangle EGH is 6 units.

Find out more on similar triangles at: https://brainly.com/question/2644832

Given: △EGH ~ △IKL, HF and LJ are medians. HE = 9, LI = 6, HF = x+2, and LJ = 2x−4Find: HF

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What are similar triangles?

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Given:

△EGH ~ △IKL, HF and LJ are medians. HE = 9, LI = 6, HF = x+2, and LJ = 2x−4

Find:

HF