# In an isosceles triangle ABC with base AC, BH is the height. Find BH if the perimeter

September 14, 2021 | education

| **In an isosceles triangle ABC with base AC, BH is the height. Find BH if the perimeter of triangle ABC is 87 cm, and the perimeter of triangle BHC is 45 cm.**

Since triangle ABC is isosceles and its perimeter is 87, it means AB = BC, and AC = 87 – 2BC.

The height BH divides AC in half, respectively, AH = HC = (87 – 2BC) / 2.

The area of a triangle BHC is 45 cm.

Let’s make the equation:

BC + (87 – 2BC) / 2 + BH = 45;

We solve the equation:

2BC / 2 + (87 – 2BC) / 2 + BH = 45;

(2BC + 87 – 2BC) / 2 + BH = 45;

87/2 + BH = 45;

43.5 + BH = 45;

BH = 45-43.5;

BH = 1.5.

Answer: The length of the height BH is 1.5 centimeters.

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