# The length of the rectangle is 6 cm more than its width, find the sides of the rectangle if the area is 112 cm2.

June 26, 2021 | education

| Let x cm – one side of the rectangle, then the other side will be equal to (x + 6) cm. the area is the product of the sides and it is 112 cm2, then we get the equation:

x * (x + 6) = 112,

x ^ 2 + 6x = 112,

x ^ 2 + 6x – 112 = 0.

To solve, we calculate what the discriminant is equal to:

D = b ^ 2 – 4ac,

D = 36 – 4 * (-112) = 36 + 448 = 484.

Find the roots of the equation:

x = (-b ± √D) / 2a

x = (-6 ± 22) / 2

x1 = -14, x2 = 8.

Length can only be positive.

Then the length will be:

8 + 6 = 14 (cm).

Answer: the sides are 8 cm and 14 cm.

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