Answer:
Dimension: 2ft by 3ft
Explanations:
Let the length of the rectangle be L
Let the width of the triangle be W
The formula for calculating the area of a rectangle is expressed as:
A = LW
Since the area of the room is 6 square feet, hence;
6 = LW ..................................1
If the width of a rectangular room is 1 foot less than the length, then;
W = L - 1 ...............................2
Substitute equation 2 into 1 to have:
6 = L(L - 1)
6 = L² - L
Swap sides
L² - L = 6
L² - L - 6 = 0
Factorize the resulting quadratic expressions:
L² - 2L + 3L - 6 = 0
L(L - 2) + 3(L - 2) = 0
(L + 3)(L - 2) = 0
L + 3 = 0 and L - 2 = 0
L = -3 and L = 2
Since the dimension cannot be negative, hence L = 2ft
Recall that LW = 6
W = 6/L
W = 6/2
W = 3ft
Hence the dimension of the room will be 2 feet by 3 feet