Answer:
t needs 68 feet to enclose the garden.
Step-by-step explanation:
In this problem, we are to solve the sides of a parallelogram ABCD to know the measurement to enclose a garden.
Take note that a parallelogram has two equal lengths and two equal widths. Let us assume that the parallelogram AB = CD is the length and AD = BC is the width.
Solving the problem
First, let us solve for r using the condition AD = BC
AD = BC
3r + 8 = 2r + 12
Simplify the equation
3r - 2r = 12 - 8
r = 4
Next, let us substitute the value of r to AB, BC, CD, and AD.
For AB:
AB = 4r - 2
AB = 4(4) - 2
AB = 16 - 2 = 14
For BC:
BC = 2r + 12
BC = 2(4) + 12
BC = 8 + 12 = 20
For AD:
AD = 3r + 8
AD = 3(4) + 8
AD = 12 + 8 = 20
For CD:
But AB = CD Therefore, CD = 14
Finally, let us solve the perimeter of the parallelogram
Perimeter = AB + BC + CD + AD
Perimeter = 14 + 20 + 20 + 14
Perimeter = 68 feet
Therefore, the fencing needed to enclose the garden is 68 feet.
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