The flank of an isosceles triangle refers to the base as 13:10. Find the height of the triangle

The flank of an isosceles triangle refers to the base as 13:10. Find the height of the triangle drawn to the base if the perimeter of the triangle is 72 cm.

1. Vertices of the triangle A, B, C. AB = BC. ВН – height.

2. According to the condition of the problem AB: AC = 13:10 Therefore, AB = 13AC / 10 cm.

3. Calculate the lengths of the sides of a given triangle. For the calculation, we use the calculation formula

perimeter:

AB + BC + AC = 72.

AB = BC according to the condition of the problem.

Therefore, we replace BC with AB in this expression:

2AB + AC = 72.

We substitute 13AC / 10 instead of AB in the resulting expression:

2 x 13АС / 10 + АС = 72.

36АС = 720.

AC = 20 cm.

AB = 13AC / 10 = 13 x 20/10 = 26 cm.

4. The height of the VN, according to the properties of an isosceles triangle, also performs functions

the median, that is, it divides the side to which it is drawn into equal

segments. Therefore, AH = CH = AC: 2 = 10 cm.

5. We calculate the length of the HВ height. For the calculation, we use the Pythagorean theorem:

BH = √AB² – AH² = √26² – 10² = √676 – 100 = √576 = 24 cm.

Answer: BH height is 24 cm.