Finding the Side-lengths of a Rectangle with Given Area Increase

[paech]

Homework Statement

A rectangle is 2 metres longer than it is wide. On the other hand, if each side of the rectangle is increased by 2 metres, then the area increases by 24 square metres. Find the side-lengths of the rectangle.

Homework Equations

The Attempt at a Solution

So my thoughts on dealing with this problem are to let the width = x , then the length = x + 2

The area of a rectangle is length multiplied by width, so I figured $x(x+2) + 24 = 2x + 2(x+2)$

I thought that this would make sense but it doesn't really when I try to solve for x.

 

[symbolipoint]

width=x, length=x+2, area would be x(x+2)

On the other hand, if each dimension is increased by 2, then:
width = (x)+2, and length = (x+2)+2, and area would be (x+2)((x+2)+2)
or, taking care of calculation through grouping symbols,
width = x+2 and length = x+4, and area would be (x+2)(x+4)

Notice that part of the problem description specified a difference in area between the original rectangle and the augmented rectangle, of 24 square meters.

 

[paech]

Thank you.