The base of an isosceles triangle is 12 cm, and the height drawn to it is 8 cm.
| April 1, 2021 | education
The base of an isosceles triangle is 12 cm, and the height drawn to it is 8 cm. Find the side of the triangle if the height drawn to it is 6 cm.
Since AH is the height, the triangle ACН is rectangular, in which the length of the leg AH is half the hypotenuse AC, then the angle ACB = 30. Let’s construct the height of the BH, which is also the median of the isosceles triangle ABC, then AK = AC / 2 = 12/2 = 6 cm.
In a right-angled triangle ABK, the leg ВK = 3 cm, since it lies opposite the angle 30, then, according to the Pythagorean theorem, AB ^ 2 = AK ^ 2 + ВK ^ 2 = 36 + 9 = 45.
AB = 3 * √5 cm.
Answer: The length of the side is 3 * √5 cm.
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