Question 1132871
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Let x be the length of each of the two congruent sides of the isosceles triangle.  Then, since the perimeter of the triangle is 80, the length of the base is 80-2x.<br>
The line through the vertex angle cutting the triangle in half forms two congruent triangles, each of which has two legs of lengths x and (40-x).  Since the altitude of the original triangle is the third side of both of those triangles, and since the perimeter of each of those triangles is 70, the height of the original triangle is 30.