Question

The area of a rectangle is 28m^2 and the length is 1m more than double the width. Find the dimensions

Answer 1

Explanation:

Width= x

Length= 2x + 1

Area = 28

Area =>width × length

28 = x(2x + 1)

`\begin{gathered} 28=2x^2+x \\ 2x^2+x-28=0 \\ 2x^2+8x-7x-28=0 \\ 2x(x+4)-7(x+4)=0 \\ 2x-7=0,x+4=0 \\ 2x=7,x=-4 \\ x=(7)/(2),x=-4 \end{gathered}`

width = 7/2 , -4 is invalid

`\begin{gathered} width\text{ =7/2=3.5} \\ length\text{ = 2\lparen7/2\rparen+1} \\ =7+1 \\ =8 \end{gathered}`

Therefore the dimensions are

`\begin{gathered} width=3.5\text{m} \\ length\text{ = 8m} \end{gathered}`