# 10.3.3. The Relation between the Area of Two Similar Polygons

The ratio of the perimeter of to the perimeter of is , and the sum of their areas is . Determine both areas.

• A area of , area of
• B area of , area of
• C area of , area of
• D area of , area of

### Example

The ratio of the perimeter of to the perimeter of is , and the sum of their areas is . Determine both areas.

### Solution

Since the ratio of the perimeter of to the perimeter of is , the ratio of the lengths of any two corresponding sides of and is also . The ratio of the areas of the surfaces of two similar triangles equals the square of the ratio of the lengths of any two corresponding sides of the triangles, so the ratio of the area of to the area of is . Suppose the area of is . This would mean that the area of is . Solve for as follows:

Multiply 4 by and convert to a decimal to get approximately for the area of . Multiply 25 by and convert to a decimal to get approximately for the area of .

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