The height of the triangle is 4. It divides it into two triangles with dimensions 16 and 23, respectively.

| July 3, 2021 | education

The height of the triangle is 4. It divides it into two triangles with dimensions 16 and 23, respectively. Find the perimeter of this triangle.

The first way.

The perimeter of triangle ABH is:

Equ = AB + AH + BH = 16 cm.

The perimeter of the СВH triangle is:

Рсвн = ВС + СН + ВН = 23 cm.

The perimeter of the triangle ABC is:

Add the perimeters of triangles ABH and CBH.

Equal + Rsvn = AB + BC + AH + CH + 2 * BH = 16 + 23 = 39 cm.

Equal + Rsvn = AB + BC + AH + CH + 2 * 4 = 39 cm.

AB + BC + AH + CH = 31 cm.

Ravs = AB + BC + AC = AB + BC + AH + CH = 31 cm.

Second way.

The perimeter of the triangle ABC is equal to the sum of the perimeters of the triangles ABH and CBH minus the lengths of the two heights BH.

Ravs = Equal – Rvsn – 2 * BH = 16 + 23 – 2 * 4 = 39 – 8 = 31 cm.

Answer: The perimeter of triangle ABC is 31 cm.



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