Question

The length of a rectangle is 4 meters less than twice the width. If the area of the rectangle is 286 square​ meters, find the dimensions.

Answer 1

essentially, you have A=bw for a rectangle.
286=x(2x-4), let width be x.
solve
286=2x^2-4x for x

Answer 2

The dimensions of the rectangle are length = 22 meters and width = 13 meters

What is area of rectangle?

$A=l\times w$, where 'l' is the length and 'w' is the width of the rectangle.

For given question,

Suppose 'l' is the length and 'w' is the width of the rectangle.

The length of a rectangle is 4 meters less than twice the width.

So, we get an equation,

⇒ l = 2w - 4

The area of the rectangle is 286 square​ meters.

⇒ A = 286 sq. m.

Using the formula for the area of the rectangle,

$\Rightarrow A=l\times w\\\\\Rightarrow 286=(2w-4)\times w\\\\\Rightarrow 286=2w^2-4w\\\\\Rightarrow 2w^2-4w-286=0$

Now, we solve the quadratic equation $2w^2-4w-286=0$

$\Rightarrow 2w^2-4w-286=0\\\\\Rightarrow w^2-2w-143=0\\\\\Rightarrow (w-13)(w+11)=0\\\\\Rightarrow w-13=0~~~or~~~w+11=0\\\\\Rightarrow w=13~~~or~~~w=-11$

w = -11 is not possible.

So, the width of the rectangle is 13 meters.

And the length of the rectangle would be,

$\Rightarrow l \\= 2w - 4\\=(2\times 13)-4\\=22$

Therefore, the dimensions of the rectangle are length = 22 meters and width = 13 meters

Learn more about the area of the rectangle here:

https://brainly.com/question/20693059

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