# The ratio of the side to the base of an isosceles triangle is 5: 6, and the height of the triangle

The ratio of the side to the base of an isosceles triangle is 5: 6, and the height of the triangle to the base is 12 cm. Find the sides of the triangle.

1. Vertices of the triangle – A, B, C. AB / AC = 5/6.

2. By the condition of the problem AB: AC = 5: 6. Therefore, AC = 6AB / 5 centimeters.

3. AH = 1/2 AC, since in an isosceles triangle, the height of the BH also performs the function of the median.

AH = 3AB / 5 cm.

4. AB² = AH² + BH².

AB² = AH² + BH².

AB² = (3AB / 5) ² + 144.

25АВ² – 95АВ² / 25 = 144.

16AB² / 25 = 144.

16AB² = 25 x 144.

AB² = 25 x 9.

AB = √25 x 9 = 5 x 3 = 15 cm.

AC = 6AB / 5 = 6 x 15/5 = 18 cm.

Answer: AC = 18 cm, BC = AB = 15 cm.

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