# In an isosceles triangle, the side is 15 cm and the base is 24 cm. Find the height dropped on the base.

July 30, 2021 | education

| It is known:

Isosceles triangle ABC;

BК – height;

Lateral side AB = BC = 15 cm;

AC base = 24 cm.

Let’s find the height BK.

1) In an isosceles triangle ABC, the height BK to the base of the AC divides the base of the AC in half.

2) Find the side of the CК.

SK = 1/2 * AC = 1/2 * 24 cm = 24/2 cm = 12 cm;

2) Consider a triangle BKC. The triangle is rectangular. Angle K = 90 °.

Find the leg BK by the Pythagorean theorem.

BK = √ (BC ^ 2 – CK ^ 2) = √ (15 ^ 2 – 12 ^ 2) = √ ((15 – 12) * (15 + 12)) = √ (3 * 27) = √81 = 9 ;

This means that the height BK = 9 cm.

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