Let's start by defining variables.
P = perimeter
L = length
W = width.
For a rectangle, P = 2L + 2W.
But what are the measures of L and W? Let's begin by translating English in math:
"Twice the Width" is 2W
"2 cm longer than twice the width": 2W + 2
"The length" "is" "2 cm longer than twice the width"
L = 2W + 2
or, L = 2W + 2. Great! we can now use 2W + 2 in place of L in the formula for the perimeter:
P = 2L + 2W. Substitute:
P = 2(2W + 2) + 2W. Distribute the 2:
P = 4W + 4 + 2W. Gather like terms:
P = 6W + 4.
Now substitute known values:
40 = 6W + 4. subtract 4 from both sides:
36 = 6W. Divide both sides by 6:
6 = W.
The formula for the area of a rectangle is L*W, so we still need to find L. Fortunately, we know that
L = 2W + 2. Substitute:
L = 2*6 + 2
L = 14
Now, we can find the area:
A = L * W
A = 6 * 14.