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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?

User Nissim
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1 Answer

4 votes

Answer: The width is x + 4

Step-by-step 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* w

where w represents the width.

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


w=(A)/(l)

Replacing the expressions given:


w=(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*7=28

Then, the expression is:


w=(\left(x+4\right)\left(x+7\right))/(x+7)

Simplifying:


w=(x+4)((x+7))/(x+7)
w=(x+4)*1

Then the width is x + 4.

User Johnny Thunderman
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