Question

The area of a rectangle is 66m^, and the length of the rectangle is 1 m more than double the width. Find the dimensions of the rectangle.

Answer 1

Given: The area of a rectangle is 66 m², & the length of the rectangle is 1 metre more than twice the width of rectangle.

Need to find: The dimensions of the rectangle?

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❍ Let's say, width of the rectangle be x metre.

Then, length of rectangle be (2x + 1) metre.

width of rectangle = x

`\begin{gathered} (2x+1)x=66 \\ 2x^2+x=66 \\ 2x^2+x-66=0 \\ 2x^2+12x-11x-66=0 \\ 2x(x+6)-11(x+6)=0 \\ (2x-11)(x+6)=0 \\ 2x-11=0,x+6=0 \\ 2x=11,x=-6 \\ x=(11)/(2)=5.5,x=-6 \end{gathered}`

Dimensions of the rectangle can't be —ve. Hence, x = 11/2 = 5.5 metres.

Therefore,

Width of rectangle, x = 5.5 m

Length of rectangle, (2x + 1) = 2(5.5 + 1) = 12 m.

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Hence the dimension of the rectangles are 12m and 5.5m respectively.