Answer:
14 square units
Step-by-step explanation:
You need to know the formulas for the perimeter of a rectangle and the area of a rectangle, which are
2L + 2W - P where L is the length, W is the width, and P is the perimeter
and
A = LW
So we need to find the length and width to find the area
Step 1: Write equations out of the given information
"The length of a rectangle is 1 more than 3 times the width" can be rewritten as
L = 3W + 1
"the perimeter of the rectangle is 18 units" can be rewritten as
2L + 2W = 18
Step 2: Plug the first formula into the second one and solve
2(3W + 1) + 2W = 18
Simplify...
6W + 2 + 2W = 18
Combine like terms and subtract 2 from both sides
8W = 16
Divide both sides by 8 to isolate the W
W = 2
Step 3:
Plug W = 2 into the formula for L and solve for L
L = 3(2) + 1
L = 6 + 1
L = 7
Step 4: Use the length and width to calculate the area
A = LW
A = (7)(2)
A = 14 units squared
