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 =
You have 2 free calculationss remaining
How does the Rectangle Word Problem Calculator work?
Free Rectangle Word Problem Calculator - Solves word problems based on area or perimeter and variable side lengths
This calculator has 5 inputs.
This calculator has 5 inputs.
What 4 formulas are used for the Rectangle Word Problem Calculator?
Set a variable for length
Set a variable for width
Figure out if you are solving for perimeter or area
See if you can express one variable in terms of another
For more math formulas, check out our Formula Dossier
Set a variable for width
Figure out if you are solving for perimeter or area
See if you can express one variable in terms of another
For more math formulas, check out our Formula Dossier
What 4 concepts are covered in the Rectangle Word Problem Calculator?
- area
- Number of square units covering the shape
- perimeter
- The distance around a shape or object
- rectangle
- a quadrilateral with four right angles
- rectangle word problem
- a mathematical problem expressed entirely in words involving rectangle area or perimeter typically used as an educational tool
Example calculations for the Rectangle Word Problem Calculator
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