Quadratic equations in a shaded part of a rectangle

Question

I'm assuming you have to use quadratics, but honestly I'm stumped :'(

 

Word question:

The diagaram shows the dimensions of a rectangle cut out of a larger rectangle, the smaller one is height 2 by width x. The remains have height of x and width of x+1. What is the area of the not cut out part of the larger rectangle.

Answer 1

If I've pictured this right, we have one rectangle inside another. We want the area between the inner and outer rectangles. The area of the inner rectangle is 2x while the area of the outer rectangle is x(x+1)=x^2+x. No matter how the inner rectangle is positioned, the area between it and the outer rectangle is always the same and it is x^2+x-2x=x^2-x=x(x-1). Note that if x=1 the two rectangles have the same size.

Comments

Unfortunately my tablet didn't show the picture so I had to rely on imagination, and I had no figures to work with.

Answer 2

Let the area of the largest rectagle be A, the blank rectangle cut out be B, and the shaded shape of letter "L" be C. Thus, we have: A-B=C Here, C=6, so A-B=6 From the diagram, we have: A=x(x+1) and B=2x So, the equation, A-B=6, can be rewritten: x(x+1)-2x=6 Simplify the equation,getting x^2-x-6=0 Factor the equation,getting (x-3)(x+2)=0 From the diagram, x>2 so x+2≠0 Thus, we have: x-3=0 That is: x=3 The answer is: x=3