Question

The length of a rectangle is 23 centimeters less than four times its width. Its area is 72 square centimeters. Find the dimensions of the rectangle The width is The length is

Answer 1

Let the width be x

The lenght will be 4x-23

The area is lenghtX width, so:

x(4x-23) = 72

4x² -23x -72=0

Using the quadratic formula:

`\begin{gathered} x=\frac{-b\pm\sqrt[\square]{b^(2)-4ac}}{2a} \\ x=\frac{23\pm\sqrt[\square]{529+1152_{}}}{8} \\ x=(23\pm41)/(8) \\ x1=8 \\ x2=-18/8 \end{gathered}`

We'll use the value of x1, because we're looking for a measure, so it has to be positive.

Then, the width is 8cm. The lenght is 4*8-23= 9cm.