The length of the rectangle was reduced by 4 cm and got a square, the area of which is 12 cm² less

| June 18, 2021 | education

The length of the rectangle was reduced by 4 cm and got a square, the area of which is 12 cm² less than the area of the rectangle. Find the side of the square.

1. Take x (cm) as the length of the side of the square.

2. The length of the rectangle (x + 4) cm. The width of the rectangle is x cm, since after its length was reduced by 4 cm, its width became equal to the length of the side of the square.

3. The area of a rectangle is the product of the lengths of its two sides:

x (x + 4) = (x² + 4x) cm².

4. The area of a square is the product of the lengths of its two sides: x² cm².

5. Considering that the area of the square is 12 cm² less than the area of the rectangle, we will make the equation:

(x² + 4x) – x² = 12;

4x = 12;

x = 3 cm.

Answer: the length of the side of the square is 3 centimeters.



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