Question

The sum of the areas of two similar polygons is 65 square units. If their perimeters are 12 units and 18 units, respectively, what is the area of the larger polygon?

Answer 1

Thanks for the query.

Let us consider that the sides of the polygons are in the ratio of 1 : k

Then their areas will be in the ratio 1 : k^2
Their perimeter will be in the ratio 1 : k
Therefore, 1 / k = 12 / 18
k = 3 / 2
Hence Area of polygon 1 + Area of polygon 2
= Area of polygon 1 + k^2 * Area of polygon 1 (since the Areas are in the ratio of 1 : k^2)
=> Area of polygon 1 + (9 / 4)* Area of polygon 1 = 65
Solving we get Area of polygon 1 >>> 20 sq units
and Area of polygon 2 >>> 20*(9 / 4) = 45 sq. units