In a triangle with sides of 3 inches, 4 inches and 5 inches, the height is drawn to the larger side.

In a triangle with sides of 3 inches, 4 inches and 5 inches, the height is drawn to the larger side. Find the segments into which the height divides this side.

In the triangle ABC, the Pythagorean theorem is satisfied: AB ^ 2 = AC ^ 2 + BC ^ 2.

25 = 16 + 9 = 25.

Then triangle ABC is rectangular.

Let’s define the area of the triangle ABC.

Saws = AC * BC / 2 = 4 * 3/2 = 6 dm2.

Also, the area of the triangle ABC is equal to: Savs = AB * CH / 2.

CH = 2 * Savs / AB = 2 * 6/5 = 12/5 dm.

From the right-angled triangle ВСН, according to the Pythagorean theorem, we determine the length of the leg ВН.

BH ^ 2 = BC ^ 2 – CH ^ 2 = 9 – 144/25 = 81/25.

BH = 9/5 = 1 (4/5).

Then AH = AB – BH = 5 – 9/5 = 16/5 = 3 (1/5) dm.