# geometry

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how do you find the height of an isosceles triangle only knowing the lengths of all three bases?

EX: There's isosceles triangle ABC with vertex angle B. AB= 5x-28. BC= 2x+11. AC= x+5

• geometry -

The triangle is isoceles, so there will be 1 base and 2 sides of equal length. A perpendicular line segment from the base to the vertex of the other 2 sides (aka the height) will also be the midpoint of the base. You then have a right triangle, with the hypotenuse being the side length, and the base being 1/2 the base of the isoceles triangle.

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