# One side of the rectangle is 9cm smaller than the other, and its area is 70cm². Find the sides of the rectangle.

August 27, 2021 | education

| As we know, a rectangle is a geometric figure with right angles, in which the parallel sides are equal (not to be confused with a square, in which all sides are equal).

The area of the rectangle is found by the formula: S = a * b, where a is the length and b is the width. Since we know the area, we get that 70 cm² = ab.

Suppose that b <a by 9 cm, it turns out that a = b + 9. Substitute in the area formula:

70 cm² = b * (b + 9);

70 cm² = b² + 9b.

b² + 9b – 70 = 0.

D = 81 – 4 * 1 * (-70) = 361.

b1 = (-9 + 19) / 2 = 5.

b2 = (-9 – 19) / 2 = -14 does not fit according to the problem statement, b> 0.

Since b = 5 cm, then a = 5 + 9 = 14 cm.

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