Answer:
The answer is below
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.
