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The areas of two similar triangles are 72dm^2 and 50dm^2. The sum of their perimeters is 226dm. What is the perimeter of each of these triangles?


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calculista

Answer:

Per2 = 102.727 dm

Per1 = 123.272 dm

Step-by-step explanation:

We know that the area of similar triangles are related to the square of their perimeters.

This means that

(Per1^2)/(Per2^2)  =  Area1 / Area2

If we take the square root of the previous equation

(Per1)/(Per2)  =  [tex]\sqrt{Area1 / Area2}[/tex]

(Per1)/(Per2)  =  [tex]\sqrt{72/ 50}[/tex]

(Per1)/(Per2) = 1.2

We also know that

Per1 + Per2 = 226 dm

So,

1.2*Per2 + Per2 = 226 dm

2.2*Per2 = 226 dm

Per2 = 102.727 dm

Per1 = 1.2*Per2 = 123.272 dm

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