The perimeters of two similar polygons are 4: 7, and the area of the smaller one is 48. Find the area of the larger polygon.

It is known from the condition that the perimeters of two similar polygons are related as 4: 7. It is also known that the area of ​​the smaller polygon is 48. In order to find the area of ​​the larger polygon, we compose and solve the equation.

So, the ratio of the perimeters of the rectangles is the coefficient of similarity. In this problem, the similarity coefficient is 4/7.

The ratio of the areas of similar polygons is equal to the square of the similarity coefficient.

We get equality:

48 / x = (4/7) ^ 2;

48 / x = 16/49;

We are looking for an unknown divisor:

x = 147.

Answer: 147 the area of ​​the larger polygon