ABCD – parallelogram, AD = 12 cm, perimeter of the triangle BOC = 27 cm. Find AC + BD.

The parallelogram diagonals BD and AC are halved at the intersection point O:

BO = BD / 2;

CO = AC / 2.

The opposite sides of the parallelogram are equal: AD = BC = 12 cm.

BO + OC + BC = 27;

BO + OC = 27 – BC = 27 – 12 = 15;

Instead of BО and СО, we substitute the found expressions:

BD / 2 + AC / 2 = 15;

BD + AC = 30.

Answer: AC + BD = 30 cm.