David currently has a square garden. He wants to redesign his garden and make it into a rectangle with a length that is 4 feet shorter than twice its width. He decides the perimeter should be 60 feet.
Determine the dimensions, in feet, of his new garden. What would be the equation? Would it be 2w-4=60?
But then when I do the perimeter for the width and length I would get more than 60.
Two equations
L = 2 W - 4
2 L + 2 W = 60
so
2 (2W-4) + 2 W = 60
4 W - 8 + 2 W = 60
6 W = 68
W = 11 1/3 = 11 feet 4 inches
L = 22 2/3 - 4 = 18 2/3 = 18 feet 4 inches
Oh never mind I see what I did to make it more than 60.
But wait. How did you get the dimensions for the length and width the way you did?
well, 68/6 is 11.3333333333
and
2(11.333 etc) - 4 is 18.66666666
I will add some comments
Two equations
L = 2 W - 4 given
2 L + 2 W = 60 perimeter of rectangle = 2W+2L
so
2 (2W-4) + 2 W = 60 Use (2W-4) for L
4 W - 8 + 2 W = 60 multiply parentheses out
6 W = 68 adding 8 to both sides and combining like terms
W = 11 1/3 = 11 feet 4 inches dividing by 6
L = 22 2/3 - 4 = 18 2/3 = 18 feet 4 inches by going back to L=2W-4
To determine the dimensions of David's new garden, let's assign variables to its dimensions. Let's use 'w' to represent the width of the garden.
According to the problem, the length of the garden is 4 feet shorter than twice its width. So, the length can be calculated as (2w - 4).
The perimeter of a rectangle is given by the formula: Perimeter = 2 * (length + width). In this case, the perimeter is given as 60 feet. Therefore, we can write the equation as:
2 * [(2w - 4) + w] = 60
Simplifying this equation will help us determine the dimensions of the new garden.