The side of an isosceles triangle is 17 cm, and the height drawn to it is 8 cm. Find the base of the triangle.

1) ∆ABS is isosceles. AB = BC = 17 cm.

АН – height to the BC side. Hence ∆АВН is rectangular.

By the Pythagorean theorem, we have AB ^ 2 = AH ^ 2 + BH ^ 2 or BH = √ (AB ^ 2 – AH ^ 2) = √ (172 – 82) = √225 = 15 cm.

ВС = ВН + СН or СН = ВС – ВН = 17 – 15 = 2 cm.

АН – height to the BC side. Hence ∆АСН is rectangular.

By the Pythagorean theorem, we have AC ^ 2 = AH ^ 2 + CH ^ 2 or AC = √ (AH ^ 2 + CH ^ 2) = √ (8 ^ 2 + 2 ^ 2) = √68 = 2√17 cm.

Answer: AC = 2√17 cm.