Respuesta :
Annie and Bronwyn buy two rectangles of material.
The width is common and it is x+2.
The height of Annie's rectangle is x+3, the height of Bronwyn is 5.
Since the area of a rectangle is the product of width and height, Annie's rectangle has an area of
[tex]A = (x+2)(x+3)[/tex]
And Bronwyn's rectangle has an area of
[tex]B = 5(x+2)[/tex]
If Annie bought more than Bronwyn, the difference is
[tex]A-B = (x+2)(x+3)-5(x+2) = (x+2)[(x+3)-5] = (x+2)(x-2)[/tex]
You can write this expression as you prefer: [tex](x+2)(x-2)=x^2-4[/tex]
Question (d) represents the situation
[tex]A=B+5 \implies (x+2)(x+3)=5(x+2)+5[/tex]
We can manipulate and solve this equation as follows:
[tex](x+2)(x+3)=5(x+2)+5 \iff x^2+5x+6=5x+15 \iff x^2-9=0 \iff x = \pm 3[/tex]
We can't accept the solution x = -3 because it would lead to negative dimensions. So, we have x=3, which implies the following dimensions and area:
[tex]A = (x+2)(x+3) = 5\cdot 6 = 30[/tex]
[tex]B = 5(x+2) = 5\cdot 5 = 25[/tex]
which indeed means that Annie has 5 squared meters more material than Bronwyn.
