Question

RESOLVE IF POSSIBLE. IF NO, INDICATE THE INFORMATION NEEDED. The width of a rectangle is 6 inches less than its length. The area of the rectangle is 135 inches². Find the length and width.

Answer 1

Let's take the length as x and the width as y.

According to the statement, the width is 6 less than the length, it means the width is x-6. It is also said that the area is 135, it means that the width times the length is 135.

Use this information to find the length and the width.

`y=x-6`
`\begin{gathered} A=x\cdot y=135 \\ x\cdot(x-6)=135 \end{gathered}`

Write the quadratic equation:

`x^2-6x-135=0`

Solve for x (use the quadratic formula):

`\begin{gathered} x_{}=(-\left(-6\right)\pm√(\left(-6\right)^2-4\cdot\:1\cdot\left(-135\right)))/(2\cdot\:1) \\ x_{}=(-\left(-6\right)\pm\:24)/(2\cdot\:1) \\ x_{}=(-\left(-6\right)+24)/(2\cdot\:1),\: x_{}=(-\left(-6\right)-24)/(2\cdot\:1) \\ x=15 \\ x=-9 \end{gathered}`

In this case, we have to use only positive values of x, because the length of a rectangle can not be negative. It means, the length of the rectangle is 15 and the width (which is 6 inches less) is 9.

Length=15 inches

Width=9 inches