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

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.