Sam recently has a Square garden. He wants to redesign his garden and make it into a rectangle with a length that is 3 feet shorter than twice it's width. He decides that the perimeter should be 60 feet. What are the dimensions,in feet, of his new garden.
2L + 2W = P
2L + 2W = 60
L = 2W -3
2(2W-3) + 2W = 60
4W -6 + 2W = 60
6W = 66
w = 11
Can you find L?
To find the dimensions of Sam's new rectangle garden, we can set up an equation based on the given information.
Let's say the width of the rectangle is "x" feet. According to the problem, the length of the rectangle is 3 feet shorter than twice its width, so the length would be (2x - 3) feet.
The perimeter of a rectangle can be found by adding up all four sides. In this case, the perimeter is given as 60 feet.
So, we can set up the equation:
Perimeter = 2 * (Length + Width)
Plugging in the values we have:
60 = 2 * ((2x - 3) + x)
Now we can solve for "x":
60 = 2(3x - 3)
Divide both sides by 2:
30 = 3x - 3
Add 3 to both sides:
33 = 3x
Divide both sides by 3:
11 = x
So, the width of the rectangle is 11 feet.
Now we can find the length by substituting the value of "x" back into our expression for the length:
Length = 2x - 3
Length = 2(11) - 3
Length = 22 - 3
Length = 19 feet
Therefore, the dimensions of Sam's new rectangle garden are 11 feet in width and 19 feet in length.