The length of a rectangle is 3 feet more than its width. The area of the rectangle is 18 square...

Question:

The length of a rectangle is 3 feet more than its width. The area of the rectangle is 18 square feet. What are the length and width of the rectangle?

The Area of a Rectangle:

A rectangle is a closed geometrical figure that has two pairs of parallel sides. The parallel sides of a rectangle are congruent, but the adjacent sides are not. For example, a football pitch is a figure with a rectangular shape. The area of a rectangle is determined by multiplying the length by the width of the rectangle {eq}(A = l\times w) {/eq}.

Answer and Explanation:


The area of a rectangle is given by:

  • {eq}A = l\times w {/eq}, where {eq}l {/eq} is the length and {eq}w {/eq} is the width.

Given that a rectangle's length is 3ft more than its width, we can express the length as:

  • {eq}l = w + 3 {/eq}

Therefore, the area becomes:

  • {eq}A = (w + 3)\times w {/eq}
  • {eq}A = w^2 + 3w {/eq}

If the area is 18 square feet, then:

  • {eq}18 = w^2 + 3w {/eq}
  • {eq}w^2 + 3w - 18 = 0 {/eq}

We have a quadratic equation to solve.

Factoring the equation, we get:

  • {eq}w^2 + 6w - 3w - 18 = 0 {/eq}
  • {eq}w(w + 6) - 3(w +6) = 0 {/eq}
  • {eq}(w - 3)(w + 6) = 0 {/eq}
  • {eq}w = 3\; \rm ft, \quad w = -6\; \rm ft {/eq}

Considering the positive value of w, the width of the rectangle is:

  • {eq}\boxed{\color{blue}{w = 3\; \rm ft}} {/eq}

And the length is equal to:

  • {eq}l = w + 3 {/eq}
  • {eq}\boxed{\color{blue}{l = 3 + 3 = 6\; \rm ft}} {/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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