# The perimeter of an isosceles triangle ABC is 16, its base is AC = 6. Find the height AH of the triangle.

August 18, 2021 | education

| The perimeter of a triangle is equal to the sum of the lengths of its sides. P = AB + BC + AC. Our triangle is isosceles, and sides AB and BC are equal.

P = 2AB + AC;

2AB = P – AC;

AB = (P – AC) / 2;

AB = (16 – 6) / 2 = 10/2 = 5.

BО – height, it is the median in an isosceles triangle. and the bisector. This means that point O is the middle of the AC. OС = 6/2 = 3.

The BОС triangle is rectangular. It knows the hypotenuse BC = 5, leg OС = 3. Find the second leg BO, which is the height of the triangle ABC, according to the Pythagorean theorem.

BC ^ 2 = BO ^ 2 + OC ^ 2;

BO * 2 = BC ^ 2 – OC ^ 2;

BO ^ 2 = 5 ^ 2 – 3 ^ 2 = 25 – 9 = 16;

BO = 4.

Answer. 4.

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