To answer this question we need to know a few key concepts.
- A rectangle has 4 sides.
- The perimeter of a rectangle is equal to : 2L (the length of 2 sides) + 2W (the width of 2 sides)
- Therefore the formula for the perimeter of a rectange is : P = 2L + 2W
We will use these concepts to from an equation based on what we know.
- We know that the perimeter is 84 ft.
- We know that the length is 2 ft more than the width.
We will let length = 2L
We will let width = 2W
Therefore our equation will be: 2L + 2W = 84
Since we know that the length is 2 ft more than the width , then we know that L= W +2
We can substitute W+2 for L in our equation.
Therefore our equation becomes: 2(W+2) + 2W = 84
We can simplify our equation using the distributive property.
Our equation becomes: 2W +2W +4 -84 or 4W + 4 = 84
We want to isolate our unknown variable (4L) on one side of the equation.
To isolate 4L we will subtract 4 from both sides of the equation.
4W + 4 -4 = 84-4 (Remember whatever opearation we perform on one side of the equation, we must perform the same identical operation on the other side fo the equation).
Our eqation becomes 4W =80
To solve for W(width) we divide both sides of the equation by 4.
4W/4 = 80/4
W = 20
Therefore L = W +2 = 20 +2 or 22..
The width is 20 ft.
The length is 22 ft.
The final step in solving any equation is to substitute the values into our equation to ensure they satisfy it.
Our equation P(perimeter) = 2L (length) + 2W (width)
2(22) + 2 (20) = 84
44 + 40 = 84
Our solution satisfies our equation, (formula).
The garden is 22 ft. long and 20 ft. wide.