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A rectangle's width is x and its length is 2x-1. Its area is 21. Find its dimensions.

my work so far: 21 = x(2x +1) 21 = 2x^2 + x I was wondering how I would continue to solces this problem.

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Length of the rectangle : 6 unit

Width of the rectangle : 3.5 unit

We have width of the rectangle is x and length is 2x-1.

Area of the rectangle = 21.

We know area of the rectangle = Length ×width

So,

\(21 = (2x-1)x\\21=2x^{2} -x\\2x^{2} -x-21=0\\2x^{2} -7x+6x-21=0\\x(2x-7)+3(2x-7)=0\\(x+3)(2x-7)=0\\x=-3,x=\frac{7}{2}\)

Since the width cannot be negative. So width x=3.5 unit

Now, Length

\(=2x-1\\=2(\frac{7}{2} )-1\\=7-1\\=6\)

Therefore width is 3.5 unit and length is 6 unit of the rectangle.

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