# A triangle with a perimeter of 24 cm is divided into two triangles in height, the perimeters

A triangle with a perimeter of 24 cm is divided into two triangles in height, the perimeters of which are 14 cm and 18 cm. Find the height of the triangle.

Let’s denote the perimeters of the triangles by Р1, Р2, Р3.

P1 = AB + BC + AC = AB + BC + AH + CH = 24 cm.

P2 = AB + AH + BH = 18 cm.

Р3 = ВС + СН + ВН = 14 cm.

Of the last two equations, we express AB + AН in the first, and BC + CH in the second equation.

AB + AН = 18 – ВН.

ВС + СН = 14 – ВН.

Let’s substitute them in the first equation.

18 – ВН + 14 – ВН = 24 cm.

2 * ВН = 8.

BH = 8/2 = 4 cm.

Answer: The HВ height is 4 cm.

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