Question

The length of a rectangle is 3 meters more than 2 times the width. If the area is 27 square meters, find the widthand the length.Width:___ metersLength:___ meters

Answer 1

Solution

Step 1

Let the width be x

Let the length = 2x + 3

Step 2

$\begin{gathered} Area\text{ = x\lparen2x + 3\rparen} \\ \\ 27\text{ = 2x}^2+\text{ 3x} \\ \\ 2x^2+3x-27=0 \end{gathered}$

Step 3

$\begin{gathered} 2x^2+9x-6x-27=0 \\ \\ x(2x+9)-3(2x+9)=0 \\ \\ (2x+9)(x-3)=0 \\ \\ x\text{ = 3, x = }\frac{-9}{2} \\ \\ x\text{ cannot be negative} \\ \\ x\text{ = 3} \end{gathered}$

Step 3

Width = 3

Length = 2x3 + 3 = 9

Final answer

Width = 3m

Length = 9m