Question 845205
 

So we know that the area of the rectangle is 14m^2. We also know that the length L = 2w-3 or 3m less than double the width. Whenever you see "double" that means multiply by 2. 

The area of a rectangle is 

A = L * W

Let's plug in the values that we know.

14 = (2w-3) * w 


Combine like terms and use the distributive property.

14 = 2w^2 - 3w. 

Now we have a quadratic equation, but to solve for the root of the equation, w, we need to make the left side of the equation zero. We do that by subtracting 14 from both sides to get 

0 = 2w^2-3w - 14 

Now, we use the quadratic formula to solve for w.

*[invoke quadratic "x", 2, -3, -14 ]

Therefore the roots are (-2,0) (3.5, 0).

We can discard the negative root since you can't have a negative width. Therefore the width w = 3.5 and the length l = 2(3.5) - 3 = 4.

This checks out since A = 14m^2 and 3.5 * 4 = 14.