The area of two squares is 4: 9, with the side of one of these squares being 5 more than

| September 21, 2021 | education

The area of two squares is 4: 9, with the side of one of these squares being 5 more than the side of the other. Find the sizes of the squares.

1. Take as x (units) the length of the side of the smaller square. The length of the side of the larger square (x + 5) units.

2. The area of ​​the smaller square is x², (x + 5) ² is the area of ​​the larger square.

3. Considering that the areas of both geometrical figures are in the ratio of 4: 9, we will compose the proportion:

x² / (x + 5) ² = 4/9;

9x² = 4 (x² + 10x + 25);

5x² – 40x – 100 = 0;

x² – 8x – 20 = 0;

The first value x = (8 + √64 + 80) / 2 = (8 + 12) / 2 = 10 units of measure – the length of the side of the smaller square.

The second value is x = (8 – 12) / 2 = – 2. Not accepted.

The side length of another square is 10 + 5 = 15 units.

Answer: the side length of the smaller square is 10 units, the side length of the larger square is 15 units.



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