# A triangle whose perimeter is 24 in height is divided into 2 triangles whose perimeters are 14

July 24, 2021 | education

| **A triangle whose perimeter is 24 in height is divided into 2 triangles whose perimeters are 14 and 18. Find the height of this triangle.**

The perimeter of a triangle is equal to the sum of all its sides. BH is the height of the triangle.

Perimeter of triangle ABC: P = AB + BC + AC = 24 cm;

Perimeter of triangle ABH: P1 = AB + BH + AH = 14 cm;

Perimeter of triangle BCH: P2 = AC + CH + BH = 18 cm;

P = (P1 + P2) – 2 * BH;

BH = (P1 + P2 – P): 2 = (14 + 18 – 24): 2 = 8: 2 = 4 (cm).

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