Question 1132871: An isosceles triangle with perimeter 80 cm is cut in half through a line passing through its vertex angle. If each resulting triangle has a perimeter of 70 cm, find the height of the original triangle.
Found 3 solutions by Boreal, greenestamps, josgarithmetic:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! There is an original triangle with perimeter 80 cm
There are now two triangles, which together have the same perimeter as the original triangle AND also have a side not present in the original triangle, which is the altitude. Each of them has this altitude.
The total perimeter of the two triangles is 140 cm, and they differ from the original triangle by two altitudes, one in each. Therefore, the 60 cm increase is divided into two altitudes.
Each altitude is 30 cm., and that is the height of the original triangle.
Answer by greenestamps(13203)  (Show Source):
You can put this solution on YOUR website!
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.
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.
Answer by josgarithmetic(39623)  (Show Source):
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