# The height drawn to the base of the isosceles triangle is 20 cm, and to the lateral side is 24 cm. Find the perimeter of the triangle.

January 16, 2021 | education

| Given:

ABC – isosceles triangle,

AB, BC – lateral sides,

AB = BC = 24 centimeters,

ВН – height,

BH = 20 centimeters.

Find the perimeter of Ravs -?

Decision:

1) Consider a right-angled triangle ABН. Then, 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 = 24 ^ 2 – 20 ^ 2;

AH = 4√11 centimeters;

2) Consider an isosceles triangle ABC. In it AB = BC. The ВH height is also the median. Then AC = 2 * AH = 2 * 4√11 = 8√11;

3) Ravs = 24 + 24 + 8√11 = 56√11 centimeters.

Answer: 56√11 centimeters.

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