Jim and his dad are building a rectangular flower bed. they have a total of 35 feet of landscaping timber to use, and they want to use all of it. however, they are not sure what width and length they want the flower bed to be. in this activity, you will write a function in which the width of the flower bed, w, is the input, and the length, l, is the output. the perimeter of a rectangle is given by the equation 2l + 2w = p. part a jim and his dad want to find the length of the garden once they decide its width. use function notation to write a function that represents its length in terms of the width.

The perimeter is 35.  If we were to change the width, which is one of the dimensions of the flower bed, The perimeter will change.  This means that perimeter will no longer be 35.  So in order to keep the perimeter as it is, if we change one dimension, we must also change the other. Let's solve for the length, using the formula to see how much the length changes from. p = 2l + 2w 35 = 2l + 2(15) 35 = 2l + 30 5 = 2l 2.5 = l  We must increase the length from 2.5 feet.  This is because decreasing one dimension will decrease the perimeter.  But if we increase the other dimension as well, it will restore the perimeter to where is was initially.