isosceles triangle ABC,
ВН – height,
BH = 13√3.
Find the length of the side of an equilateral triangle ABC, that is, AB -?
1. Consider an equilateral triangle ABC. The HL height is also the median. Then HC = AH = AB / 2;
2. 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;
Let AB = x, then BH = x / 2;
169 * 3 + x ^ 2/4 = x ^ 2;
3 * x ^ 2 = 169 * 3 * 4;
x ^ 2 = 169 * 4;
x = 13 * 2;
x = 26.
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