math/geometry
posted by katie .
the area of one triangle is 9dm^2 and its perimeter is 4x4. The area of a similar triangle is 4dm^2 and its perimeter is 2x+6. Find the perimeter of each triangle.

For similar triangles, the ratio of the perimeters must be the square root of the ratio of areas, which is (in this case) sqrt(9/4) = 3/2
Therefore 4x4 = (3/2)(2x + 6) = 3x + 9
x = 13
The perimeter of the larger triangle is therefore 4x4 = 48 dm. That of the smaller is 2x + 6 = 32 dm 
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