SOLUTION: The Perimeters of two triangles is in the ratio of 2:4. The sum of their areas is 100 cm squared. Find the area of each triangle?

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Question 1004239: The Perimeters of two triangles is in the ratio of 2:4. The sum of their areas is 100 cm squared. Find the area of each triangle?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
That ratio is also 1:2.
Let x,y,z be the lengths of each side for the small triangle. The altitude is also in the same ratio between the two triangles (because linear measures).

Small perimeter, x+y+z
Large perimeter, 2(x+y+z)
If h is the altitude of the small triangle, the 2h is altitude for large triangle.

Small area, %281%2F2%29zh
large area, %281%2F2%292z%2A2h=%281%2F2%29%2A4%2Azh

Their summed areas is 100=%281%2F2%29zh%2B%281%2F2%29%2A4zh
200=zh%2B4zh=5zh
zh=200%2F5
zh=40
This can now be used for finding the value of each area.

Small Triangle, %281%2F2%29%2A40=highlight%2820%29
Large Triangle, %281%2F2%29%2A4%2Azh=2%2A40=highlight%2880%29