# The lateral sides of the triangle are 30cm and 25cm, and the height lowered to the base is 24cm. Find the base.

Let’s introduce the designations: AB = 25 cm, BC = 30 cm, height BD = 24 cm.

Since the height BD is perpendicular to the AC side, it is obvious that triangles ABD and CBD are rectangular with hypotenuses AB and CB, respectively, AD, BD and CD are legs.

According to the Pythagorean theorem, the sum of the squares of the legs is equal to the square of the hypotenuse.

For triangle ABD:

AD ^ 2 + BD ^ 2 = AB ^ 2;

AD ^ 2 = AB ^ 2 – BD ^ 2 = 25 ^ 2 – 24 ^ 2 = 625 – 576 = 49;

AD = √49 = 7 cm.

For triangle CBD:

CD ^ 2 + BD ^ 2 = BC ^ 2;

CD ^ 2 = BC ^ 2 – BD ^ 2 = 30 ^ 2 – 24 ^ 2 = 900 – 576 = 324;

CD = √324 = 18 cm.

Hence, AC = AD + CD = 7 + 18 = 25 cm – the required base of this triangle. One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.