Question

The area of the rectangle is given by the expression x³- 2x²- 6x + 12 and its length is given by x-2, find its (a) width (b) perimeter
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Answer 1

Given

• Area of rectangle - x³- 2x²- 6x + 12
• Length of rectangle - x - 2

To find

• Width of the rectangle

Taking note of the parameters

a) Area of rectangle => x^3 -2x^2 - 6x + 12

➯ Length of rectangle => x - 2

Since the area of the rectangle is the product of its length and width, then you can determine the width by dividing the area by the length. Factoring the area expression by grouping, we have :

Simplifying area of rectangle =>

➯ x^2(x - 2) - 6(x - 2) => (x^2 - 6)(x - 2)

So when area of rectangle is divided by length (x-2), width is (x^2 - 6)

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