Question

A carpet company uses the template to design a rug. Write an expression for the area of the shaded region as it relates to the variable length x answer.

The shaded square has a white square within it. On the outside of the shaded region there is 3x+4 on one side and x+5. On the shaded region there are four 2's on each side within the shaded.

Answer 1

area=(3x+4)(x+5)-2*2
= 3x^2+19x+16

check that

Answer 2

If the figures are squares, then
3x+4=x+5
x = 1/2
So the whole area is 5/2 by 5/2
So, two 2" squares cannot be inside.

That means that the entire area must be (3x+4)(x+5)

Take off 2 on each side, and the inner area (white) must be

(3x+4-4)(x+5-4) = (3x)(x+1)