SOLUTION: A farmer purchased 730 feet of fencing to enclose a rectangular garden. If the length of the garden is 5 feet more than 3 times the width, what are the dimensions of the garden?

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Question 202751: A farmer purchased 730 feet of fencing to enclose a rectangular garden. If the length of the garden is 5 feet more than 3 times the width, what are the dimensions of the garden?
Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website!
We'll start by finding the length and width. Then we will use these to find the diagonal. If we use "w" for the width, then the length which is "5 feet more than 3 times the width" would be (5 + 3w). The 730 feet of fencing means the perimeter of the garden is 730. Since the perimeter is the sum of the sides and since a rectangle has two equal widths and 2 equal lengths we get the following equation:
P = w + w + l + l
Substituting 730 for P and (5 + 3x) for l we get:
730 = w + w + (5 + 3w) + (5 + 3w)
Simplifying we get:
730 = 8w + 10
Subtracting 10 from both sides we get:
720 = 8w
Dividing both sides by 8 we get:
90 = w
So the width is 90 feet and the length is (5 + 3w) = (5 + 3(90)) = (5 + 270) = 275 feet.

Now we can find the diagonal since it is the hypotenuse of a right triangle formed with the width and length of the rectangle as legs. Using the Pythagorean theorem equation we get:

Simplifying we get:

Finding the square root of both sides we get: