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

July 27, 2021 | education

| **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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