Question

Factoring quadratics introThe rectangle below has an area of x2 + 11x + 28 square meters and a length of x + 7 meters.What expression represents the width of the rectangle?

Answer 1

Answer: The width is x + 4

Explanation

• The area (,A,) is:

$A=x^2+11x+28$

• The length (,l,) is:

$l=x+7$

The formula for the area of a rectangle is:

$A=l\times w$

where w represents the width.

Then, to get the width we have to isolate it in the formula:

$w=\frac{A}{l}$

Replacing the expressions given:

$w=\frac{x^2+11x+28}{x+7}$

To simplify this expression we can factor the numerator by finding two numbers that when added equal 11, and when multiplied equal 28. For example, 4 and 7:

$4+7=11$$4\times7=28$

Then, the expression is:

$w=\frac{\left(x+4\right)\left(x+7\right)}{x+7}$

Simplifying:

$w=(x+4)\frac{(x+7)}{x+7}$$w=(x+4)\times1$

Then the width is x + 4.