length and width

Question

the length of a rectangular flower garden is 5 less than twice its width. if the garden is surrounded by perimeter fencing totaling 95 yards, determine the gardens dimensions.  

Answer 1

 Let the length of the rectangular garden be L and the width of the garden be W.

 

 The length of the garden is 5 less than twice the width

 so  L = 2 W - 5  , since it is 5 less than, so we have the -5, twice the width, so we have 2 W.

 

      L = 2W - 5   let's call this equation 1

 

 Also, we are given that the perimeter of the garden is 95 yards. For a rectangular shape, we know that the perimeter is the sum the lengths and widths of the rectangle so

 

 Perimeter = 2 L + 2 W = 95 yards  let's call this equation 2

 

 Now we have 2 equations and 2 unknowns, so we can solve for the unknowns.

 

 From equation 1 we have L in terms of W, if we substitute equation 1 in equation 2 we get:

 2 ( 2W - 5) + 2 W = 95 yards, now solve for W

 

 4 W - 10 + 2 W = 95 

6 W - 10 = 95

6 W = 105

W = 105/6 = 17.5 yards

 substitute W = 17.5 in equation 1 to find L

L = 2*(17.5) - 5 = 30 yards