Answer :
This problem is an application of equations to geometry, so we need to recall some important formulas about rectangles.
Being L the length of a rectangle and W its width, the perimeter is
P = 2L + 2W
And its area is
A = L * W
Let's assume the length of the triangle is X
L = X
The problem states the width of the tarp is 6 feet less than twice the length. That is
W = 2X + 6
The perimeter of such a rectangle is:
P = 2 (X) + 2 (2X+6)
We know that value is 66, thus
2 (X) + 2 (2X+6) = 66
Apply the distributive property in the second term:
2X + 4X + 12 = 66
Joining like terms
6X + 12 = 66
Subtracting 12 in both sides
6X = 66 - 12 = 54
Solving for X
X = 54 / 6 = 9
So, the length of the tarp is 9 feet. Now find its width
W = 2 (9) + 6 = 18 + 6 = 24 feet
Finally, the area is found as
A = (9) * (24) = 216 square feet
