# One side of the rectangle is 4 cm shorter than the other. Find the sides of the rectangle if its area is 128 cm2.

May 26, 2021 | education

| By the condition of this problem, we are given a rectangle with one side four larger than the other. A rectangle has two opposite sides equal, from this it follows that we can denote the smaller unknown side by x then the other side will be equal to x + 4. By the condition of the problem, we also know the area of the rectangle, it is equal to 128. Now, knowing the formula for the area of a rectangle S = a * b we can find the sides.

128 = x * (x + 4)

128 = x + 4x

x + 4x – 128 = 0

According to the Vieta theorem, we find the roots, the negative root does not suit us and we leave 9.5, therefore the smallest side is 9.5 and the large side is 13.5.

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