Question

The width of a rectangle is 1 unit less than the length. The area of the rectangle is 72 units. What is the width, in units, of the rectangle?

Answer 1

`Length=9 units\\width=8 units`

Explanation:

Width of the rectangle= W

Length= L

W=(L-1) units

Area= 72 square units

Area of a rectangle= Length*Width

`72=L*(L-1)\\\\72=L^2-L\\\\L^2-L-72=0`

Solving the quadratic equation using the factorization method:

`L^2+8L-9L-72=0`

Taking common from the equation:

`L(L+8)-9(L+8)=0\\(L+8)(L-9)=0`

`L+8=0\\L=-8`

OR

`L-9=0\\L=9`

The length cannot be negative, therefore: Length= 9 units

`Width=Length-1\\=9-1\\=8 units`

`Length=9 units\\width=8 units`