# Point H is the base of the height drawn from the vertex of the right angle B of triangle ABC to the hypotenuse AC. Find AB if AH = 6, AC = 24.

May 31, 2020 | Education

| Consider the triangles ABC and ABH.

∠A – general

∠AHB = ∠ABC

Therefore, these triangles are similar (by similarity)

Then AC / AB = AB / AH (the hypotenuse of the large triangle refers to the hypotenuse of the small as the small leg of the large triangle to the small leg of the small triangle)

24 / AB = AB / 6

24 * 6 = AB ^ 2

144 = AB ^ 2

AB = 12

Answer: AB = 12

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