The perimeter of a rectangle is 120
The length is 6 less than 3 times the width
Calculate the Area, length, and width.
Declare Variables
We denote the Perimeter as P
the Area as A
the length as l
and the width as w
Show rectangle formulas
P = 2l + 2w
A = lw
Given
perimeter of the rectangle is 120
2l + 2w = 120
Alternate Eqution for length
l = 3w - 6
Substitute equation (2) into (1):
2(l) + 2w = 120
2(3w - 6) + 2w = 120
Simplify by removing parenthesesSimplify 2(3w - 6):
Distribute the 2 to each term in (3w - 6)
2 * 3w = (2 * 3)w = 6w
2 * -6 = (2 * -6) = -12
Our Total expanded term is 6w-12
Our new term is
6w - 12 + 2w = 120
Combine like terms:
8w - 12 = 120
Add 12 to both sides:
8w - 12 + 12 = 120 + 12
8w = 132
Divide each side by 8
| 8w | |
| 8 |
| = |
| 132 |
| 8 |
w = 16.5
Now substitute w into Equation (2):
l = 3(16.5) - 6
Simplify by removing parenthesesSimplify 3(16.5):
Distribute the 3 to each term in (16.5)
3 * 16.5 = (3 * 16.5) = 49.5
Our Total expanded term is 49.5
Our new term is
l = 49.5 - 6
l = 43.5
Calculate Area
A = lw
A = (43.5)(16.5)
A = 717.75
Final Answer
A = 717.75
P =
P =
