Mr. Parker is building a square ball room with a square dance floor surround by carpet to the wall. The room has a side length of 3x-4, and the dance floor has a side length of 2x-6. How many square meters of carpet will Mr. Parker need if x=5

Mr Parker will need a carpet of area 105 square units

Step-by-step explanation:

In this question, we are asked to calculate the area of the carpet that would be needed by Mr Parker.

Firstly, to find this area, we need to know and understand that the area of the carpet is simply the area of the room minus the area of the dance floor.

For a square, the area is L^2 where L is the length of the side of the square.

For the room, the area will be (3x -4)^2 = 3x(3x -4) - 4(3x-4) = 9x^2 -12x -12x + 16 = 9x^2 -24x + 16

For the dance floor, we have (2x-6)^2 = 2x(2x-6)-6(2x-6) = 4x^2 -12x-12x + 36 = 4x^2 -24x + 36

Thus the area of the carpet will be ⇒ (9x^2 -24x + 16) - (4x^2 -24x + 36)

= 5x^2 -20

now since x= 5

Area of carpet will be 5(5)^2 - 20 = 125 - 20 = 105 square units

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.