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: Set opposite sides equal

In a parallelogram, opposite sides are equal. So \(3r + 8 = 2r + 12\).

Step2: Solve for r

Subtract \(2r\) from both sides: \(r + 8 = 12\). Then \(r = 4\).

Step3: Find side lengths

AB: \(4r - 2 = 4(4) - 2 = 14\) ft. AD: \(3r + 8 = 3(4) + 8 = 20\) ft.

Step4: Calculate perimeter

Perimeter = \(2(AB + AD) = 2(14 + 20) = 68\) ft.

Answer:

B. 68 feet