In an isosceles triangle, the height lowered to the base is 12 dm, and the base is 18 dm. Find the side.
| September 8, 2021 | education
AB is the lateral side of the triangle that we need to find.
In an isosceles triangle, the height is the median and bisector. So the height of the VO is the median. The median is the line segment connecting the vertex to the middle of the opposite side. Therefore, point O is the middle of the AC side.
AO = AC / 2; AO = 18/2 = 9 (dm).
The ABO triangle is rectangular. Let’s apply the Pythagorean theorem to it: The square of the hypotenuse is equal to the sum of the squares of the legs. AB – hypotenuse, because lies opposite a right angle; ВO and AO are legs, because they are the sides of a right angle.
AB ^ 2 = AO ^ 2 + BO ^ 2;
AB ^ 2 = 9 ^ 2 + 12 ^ 2 = 81 + 144 = 225; AB = 15 (dm).
Answer. 15 dm.
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