Answer:
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
