The areas of two similar triangles are 72dm2 and 50dm2. the sum of their perimeters is 226dm. what is the perimeter of each of these triangles?

Step-by-step explanation:

The ratio of the linear dimensions (perimeter) is the square root of the ratio of area dimensions, so the larger : smaller ratio is ...

  √(72/50) = √1.44 = 1.2

The sum of ratio units is 1.2 + 1 = 2.2, so each ratio unit stands for ...

  (226 dm)/2.2 = 102 8/11 dm . . . . . the perimeter of the smaller triangle

Then the perimeter of the larger triangle is ...

  1.2 × 102 8/11 dm = 123 3/11 dm . . . . the perimeter of the larger triangle

Step-by-step explanation:

We know: The ratio of the areas of similar triangles is equal to the square of the similarity scale.

Threfore:

We have

Susbtitute:

We have the similarity scale.

We know: The ratio of the perimeters of similar triangles is equal to the similarity scale.

Therefore:

We have:

Substitute:

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