A rectangle has an area of . Use factoring to find possible dimensions of the rectangle. Explain why you can use factoring to find the answer.

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Step-by-step explanation:

A rectangle has an area of x² + 7x + 12. Use factoring to find possible dimensions of the rectangle. Explain why you can use factoring to find the answer.

Solution:

A rectangle is a quadrilateral (ha four sides and four angles) in which opposite sides are parallel and equal to each other. All the four angles in a rectangle are 90° each.

The area of a rectangle is given by:

Area = length * width

Hence the area is the product of two sides.

Given that:

Area = x² + 7x + 12

Factoring to find both the length and width of the rectangle:

Area = x² + 7x + 12

Area = x² + 4x + 3x + 12

Area = x(x + 4) + 3(x + 4)

Area = (x + 4)(x + 3)

After factoring we can see that the area is the product of (x + 4) and (x + 3). Hence x + 4 is the length and x + 3 is the width.

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