Question

a vegetable garden is in the shape of a parallelogram with the dimensions shown. how many feet of fencing are needed to enclose the garden? (4r - 2) ft (3r + 8) ft (2r + 12) ft 54 feet 68 feet 108 feet 140 feet

Explanation:

Step1: Use the property of parallelogram

In a parallelogram, opposite sides are equal. So, \(AB = CD\) and \(AD=BC\). Then \(3r + 8=2r + 12\).
Solve the equation \(3r+8 = 2r + 12\):
Subtract \(2r\) from both sides: \(3r-2r+8=2r - 2r+12\), we get \(r+8 = 12\).
Subtract \(8\) from both sides: \(r=12 - 8=4\).

Step2: Find the lengths of the sides

Substitute \(r = 4\) into \(AB=(4r - 2)\) ft: \(AB=4\times4-2=16 - 2=14\) ft.
Substitute \(r = 4\) into \(AD=(3r + 8)\) ft: \(AD=3\times4+8=12 + 8=20\) ft.

Step3: Calculate the perimeter

The perimeter \(P\) of a parallelogram is \(P = 2(AB + AD)\).
\(P=2(14 + 20)=2\times34 = 68\) ft.

Answer:

68 feet