The sum of the perimeters of two similar polygons is 7.8 dm. The smaller side of one polygon is 1.2 dm

| September 9, 2021 | education

The sum of the perimeters of two similar polygons is 7.8 dm. The smaller side of one polygon is 1.2 dm and the smaller side of the other is 1.4 dm. Find the perimeters of the polygons.

1. Let’s find the coefficient of similarity.

We use the lengths of the smaller sides.

1.4 / 1.2 = 7/6.

2. It is known that the ratio of the perimeters of similar polygons is equal to the coefficient of similarity,

Let P be the perimeter of the smaller polygon.

Then P * (7/6) is the perimeter of the larger one.

P + P * (7/6) = 7.8.

P * (13/6) = 7.8.

13 * P = 6 * 7.8.

P = 7.8 * 6/13.

P = 0.6 * 6.

P = 3.6 dm. is the perimeter of the smaller polygon.

P * (7/6) = 3.6 * 7/6 = 0.6 * 7 = 4.2 dm – the perimeter of the larger polygon.

Answer: The perimeters of the polygons are 4.2 in. And 3.6 in.



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