# 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

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}