Answer:
a) The perimeter of the room is the sum of the lengths of all four sides. The length of two opposite sides is 4x + 3, and the length of the other two opposite sides is 3x. Therefore, the perimeter is:
P = 2(4x + 3) + 2(3x) = 14x + 6
b) The area of the room is the product of the length, width, and height. The length is 4x + 3, the width is 3x, and the height is 3x. Therefore, the area is:
A = (4x + 3)(3x)(3x) = 27x^2 + 12x
c) If both the length and width are doubled, the new dimensions are 2(4x + 3) = 8x + 6 for the length and 2(3x) = 6x for the width.
a) The new perimeter is the sum of the lengths of all four sides:
P' = 2(8x + 6) + 2(6x) = 28x + 12
b) The new area is the product of the length, width, and height:
A' = (8x + 6)(6x)(3x) = 144x^2 + 72x
d) The new perimeter is not twice the original perimeter because:
P' = 28x + 12
2P = 28x + 12 + 28x + 12 = 56x + 24
Therefore, 2P is not equal to P', so doubling the length and width does not double the perimeter.
e) The new area is not twice the original area because:
A' = 144x^2 + 72x
2A = 2(27x^2 + 12x) = 54x^2 + 24x
Therefore, 2A is not equal to A', so doubling the length and width does not double the area.