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how do you do this (simple) algebra problem(10 pts)?

An architect designs a rectangular flower garden such that the width is exactly two-thirds of the length. If 260 feet of antique picket fencing are to be used to enclose the garden, find the dimensions of the garden? How do I do this??

Public Comments

1. ok 260ft all way round, its rectangular W=width L=Length so 1 W and 1 L = 130ft (half rectangle) so if 2/3 L = w so therefore regard it as 5 equal parts since they are all 3'rd's since its 2/3 +3/3 so divide by 5 = 26 W = 52 L = 78 (half rectangle) and just to make sure ur right, 52 + 78 + 52 +78 = 260ft
2. Take the length as X and the two thirds of this is 2/3X Perimeter = 260 feet So the preimeter of the garden algebraicly includes two times the length and width. Therefore 2(X) + 2(2/3X) = 260 feet 2X + 4/3X = 260 10/3X = 260 10X = 780 X = 78 feet Then sub X into the Length and the Width. So it will be 78 feet (Length) by (2/3 x 78) = 520 feet (Width)
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4. Okay, first you'll need to set up a basic expression that equates out. So lets start with the total fencing. The total is 260 ft, right? So what ever our expression is, it HAS to be equal to 260ft. Now, lets say that X is the length. So far we have X+(something) = 260 Now, how do we define that "something"? We know its relation ship to X is that it is 2/3 of X. So plug that in to get: X+(2/3)X=260 Now, solve for X: X(1+2/3)=260 X=260/(1+2/3) X=156ft <---- Total of both sides Length... one side of length would be: 156/2=78 We know that the width is 2/3 of X so, 156(2/3)=104 <------- Total of both sides Width... one side of width would be: 104/2=52 To double check your answer, add them together and they should equal 260! 104+156=260 Hope this helps!
5. You need to assign length variables to each side so that the width is 2/3 the length. For example, say that the length is 3x and the width is 2x. Then you use the normal formula for perimeter, which is 2L+2W=Perimeter. So you say: P = 2(3x) + 2(2x) P = 6x + 4x P = 10x Then you plug in the perimeter for P: 260 = 10x And you solve the simple algebraic function: 260/10 = 10x/10 26 = x Then you plug in for x to the length and width: L = 3x and W = 2x L = 3(26) and W = 2(26) L = 78 and W = 52