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?

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103=  p small

plarge = 123

Step-by-step explanation:

We know that the the ratio of the areas is the scale factor squared/

Larger triangle over smaller triangle

72

= scale factor ^2

50

simplify by dividing by 2 on top and bottom

36

= scale factor ^2

25

Take the square root of each side

sqrt(36)

= sqrt(scale factor ^2)

sqrt(25)

6

= scale factor

5

The ratio of the perimeters is the scale factor

p large             6

=

 p small                5

Using cross products

6 p large = 5 p small

We know the sum is 226

p large + p small = 226

p large = 226 - p small

We have 2 equation and 2 unknowns

6 p large = 5 p small

Substitute for p large

6 (226 - p small) = 5 p small

1356 - 6 p small = 5 p small

Add 6 p small to each side

1356 = 11 p small

divide by 11

1356/11 =  p small

P large = 226-1356/11

p large = 2486/11-1356/11

plarge = 1130/11

The solution requires whole number answers so

1356/11 =  p small

123.27 which rounds to 123

plarge = 1130/11

plarge = 102.7272 = 103