The length of the rectangle is 3 cm longer than the width. How long should the rectangle have

The length of the rectangle is 3 cm longer than the width. How long should the rectangle have so that its area is less than 28 cm2.

Let’s designate the width of the rectangle as x cm. Then its length will be (x + 3) cm. To find the area, you need to multiply the sides, i.e. we get x * (x + 3).

Let us find at what values ​​of x the area will be 28 cm2.

x * (x + 3) = 28,

x ^ 2 + 3x = 28,

x ^ 2 + 3x – 28 = 0. We solve the equation by first finding the discriminant, and then calculating the roots.

D = b ^ 2 – 4ac,

D = 9 – 4 * (-28) = 9 + 112 = 121.

x = (-b ± √D) / 2a

x = (-3 ± 11) / 2

x1 = -7, x2 = 4.

Those. with a side equal to 4 cm, the area will be 28 cm2. This means that for the area to be less than the specified value, the length must be less than 4 cm.

Answer: the sides must be less than 4 cm long.