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.
area=(3x+4)(x+5)-2*2
= 3x^2+19x+16
check that
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)
To find the area of the shaded region, we need to break it down into separate components and then calculate the area of each component.
We have a shaded square with a white square within it. The side length of the shaded square is (3x + 4), and the side length of the white square is 2. The area of the shaded square is (3x + 4)^2, and the area of the white square is 2^2 = 4.
Next, let's consider the lengths labeled on the outside of the shaded region. On one side, we have 3x + 4, and on the other side, we have x + 5.
To find the area of the outer rectangle that surrounds the shaded region, we multiply these side lengths. Therefore, the area of the outer rectangle is (3x + 4) × (x + 5).
Finally, to find the area of the shaded region, we subtract the area of the white square from the area of the shaded square and then subtract this result from the area of the outer rectangle. In other words, the expression for the area of the shaded region is:
(3x + 4) × (x + 5) - (3x + 4)^2 + 4