The area of a rectangle is 30 ft^2. If x + 1= width and x - 1= height, what is the value of x to...

Question:

The area of a rectangle is 30 ft^2. If x + 1= width and x - 1= height, what is the value of x to the nearest tenth of a foot?

The Area of a Rectangle:

A rectangle is a four-sided shape whose opposite sides are equal and the adjacent sides are not equal. In addition, all the interior angles of a rectangle are right angles. We calculate the area of a rectangle by multiplying the length by the width

Answer and Explanation:


The area of a rectangle is given by:

  • {eq}A = l\times w {/eq}

Given that the width is:

  • {eq}w = (x + 1)\, ft {/eq}

And the length is:

  • {eq}l = (x - 1)\, ft {/eq}

Then the area of this rectangle is:

  • {eq}A = (x + 1)(x - 1) {/eq}

If the area is {eq}30\, ft^2 {/eq}, then we have:

  • {eq}30 = (x + 1)(x - 1) {/eq}

Expanding the RHS of the equation:

  • {eq}30 = x^2 - x + x - 1 {/eq}
  • {eq}30 = x^2 - 1 {/eq}
  • {eq}x^2 = 31 {/eq}

Solving for x:

  • {eq}x = \sqrt{31} = \color{blue}{\boxed{5.57\, 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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