a vegetable garden is in the shape of a parallelogram with the dimensions shown. how many feet of fencing…

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

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

Answer

Explanation:

Step1: Use property of parallelogram

In a parallelogram, opposite - sides are equal. So (AB = CD) and (AD=BC). We have (AB=(4r - 2)) ft, (BC=(2r + 12)) ft, (CD=(4r - 2)) ft, and (AD=(3r + 8)) ft. Since (AD = BC), we set up the equation (3r+8=2r + 12). [3r+8=2r + 12] [3r-2r=12 - 8] [r = 4]

Step2: Find the lengths of the sides

Substitute (r = 4) into the expressions for the side - lengths. (AB=4r-2=4\times4 - 2=16 - 2=14) ft. (BC=2r + 12=2\times4+12=8 + 12=20) ft.

Step3: Calculate the perimeter

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

Answer:

68 feet