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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