The area of a rectangle is 72 cm^2. The length l, of the rectangle, is 6 cm longer than the...

Question:

The area of a rectangle is 72 {eq}cm^2 {/eq}. The length l, of the rectangle, is 6 cm longer than the width, w.

What is the width of the rectangle?

a) 10 cm

b) 8 cm

c) 6 cm

d) 2 cm

Rectangular Area:

The area of the rectangle is the product of the length and area. Where the length is the longer side of the rectangle and the width is the shorter side of the rectangle.

Answer and Explanation:

The width is c) 6 cm.

The area of the rectangle is {eq}\rm 72 \ cm^2 {/eq} and has a length of 6 cm longer than the width or {eq}l = w + 6 {/eq}.

Using the given information, determine the width from the formula for the area of a rectangle:

{eq}\begin{align} A &= lw \\ 72 &= w(w+6) \\ w^2 + 6w - 72 &=0 \end{align} {/eq}

Factoring:

{eq}(w +12)(w -6)=0 {/eq}

The factor that would have a positive answer is the second factor:

{eq}\begin{align} w - 6 &= 0 \\ w &= 6 \end{align} {/eq}

The width is {eq}\rm 6 \ cm. {/eq}


Learn more about this topic:

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Measuring the Area of a Rectangle: Formula & Examples

from Geometry: High School

Chapter 8 / Lesson 7
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