Solve the problem.
-Jarod is having a problem with rabbits getting into his vegetable garden, so he decides to fence it in. The length of the garden is 7 feet more than 3 times the width. He needs 46 feet of fencing to do the job. Find the length and
Width of the garden.
A) length: 22 ft; width: 5 ft
B) length: 16 ft; width: 3 ft
D) length: 19 ft; width: 4 ft

Question

Solve the problem.
-Jarod is having a problem with rabbits getting into his vegetable garden, so he decides to fence it in. The length of the garden is 7 feet more than 3 times the width. He needs 46 feet of fencing to do the job. Find the length and
Width of the garden.
A) length: 22 ft; width: 5 ft 
B) length: 16 ft; width: 3 ft 
D) length: 19 ft; width: 4 ft

Quizplus · Accepted Answer

Let's say the width is "x" feet. According to the problem, the length is 7 feet more than 3 times the width, which can be written as: length = 3x + 7.
To find how much fencing is needed, we need to add up the lengths of all four sides of the garden. Since opposite sides are equal in length, we can write:
46 = 2(length + width)
Substituting the values we know:
46 = 2(3x + 7 + x)
46 = 2(4x + 7)
46 = 8x + 14
32 = 8x
x = 4
So the width of the garden is 4 feet, and the length is 3x + 7 = 3(4) + 7 = 19 feet. So the answer is D. Let's let "w" stand for the width of the garden.

Then we're told that the length of the garden is "7 feet more than 3 times the width", which we can write as:

length = 3w + 7

We're also told that Jarod needs 46 feet of fencing. Remember that a rectangle has two lengths and two widths, so we can write:

perimeter = 2(length) + 2(width)

And we can substitute in the expressions we have for length and perimeter:

46 = 2(3w + 7) + 2w

Now we just solve for w:

46 = 6w + 14 + 2w

46 = 8w + 14

32 = 8w

4 = w

So the width of the garden is 4 feet.

To find the length, we can go back to our expression for length:

length = 3w + 7

And substitute in w = 4:

length = 3(4) + 7

length = 19

So the length of the garden is 19 feet.

Therefore, the answer is D) length: 19 ft; width: 4 ft

Solve the Problem. -Jarod Is Having a Problem with Rabbits Getting into His