The sum of the areas of the squares built on two adjacent sides of the rectangle is 369 cm 2.

| January 13, 2021 | education

The sum of the areas of the squares built on two adjacent sides of the rectangle is 369 cm 2. Find the sides of the rectangle if one of its sides is 3 cm less than the other.

1. Take for x (cm) the length of one side of the rectangle, the length of the other side (x + 3) cm.
2. Areas of the squares built on the sides of the rectangle x² cm² and (x + 3) ² cm².
3. Considering that the sum of the areas of the squares built on the sides of the rectangle is 369 cm², we compose the equation:
x² + (x + 3) ² = 369;
x² + x² + 6x + 9 = 369;
2x² + 6x – 360 = 0;
x² + 3x – 180 = 0;
The first value x = -3 + √9 + 4 x 180/2 = (- 3 + √729) / 2 = (- 3 + 27) / 2 = 12.
The second value is x = (- 3 – 27) / 2 = – 15. Not accepted.
The length of one side of the rectangle is 12 cm, the length of the other side is 12 + 3 = 15 cm.
Answer: the length of one side of the rectangle is 12 cm, the length of the other side is 15 cm.



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