An isosceles triangle is given. The height drawn to the side divides it into segments equal to 15 cm

An isosceles triangle is given. The height drawn to the side divides it into segments equal to 15 cm and 2 cm, counting from the apex of the triangle. Find the area of the triangle.

Given:
ABC – isosceles triangle,
АН – height,
BH = 15 centimeters,
HC = 2 centimeters.
Find the area of the triangle ABC, that is, S ABC -?
Decision:
1. Consider an isosceles triangle ABC. His sides are equal, that is, AB = BC = 15 + 2 = 17 (centimeters).
2. Consider a right-angled triangle ABN. By the Pythagorean theorem (the square of the hypotenuse is equal to the sum of the squares of the legs):
AH ^ 2 + BH ^ 2 = AB ^ 2;
AH ^ 2 = AB ^ 2 – BH ^ 2;
AH ^ 2 = 289 – 225;
AH ^ 2 = 64;
AH = 8.
3. S ABC = 1/2 * AN * BC;
S ABC = 1/2 * 8 * 17;
S ABC = 4 * 17;
S ABC = 68 square centimeters.
Answer: 68 square centimeters.