Find the height of a triangle with perimeter = 36cm if it breaks it into 2 triangles with perimeters 18cm and 24cm.

Given:

triangle ABC,

BH – height,

P ABC = 36 centimeters,

P ABH = 18 centimeters;

R BHC = 24 centimeters.

Find the length of the height BH -?

Decision:

Consider a triangle ABC.

P ABC = P ABH + P BHC – 2 * BH;

2 * BH = P ABH + P BHC – P ABC;

2 * BH = 18 + 24 – 36;

2 * BH = 42 – 36;

2 * BH = 6 (in order to find an unknown factor, you need to divide the product by a known factor);

BH = 6: 2;

BH = 3 centimeters.

Answer: 3 centimeters.