Answer: The lengths of the garden are 57.32 feet and 22.68 feet (approximately)
Step-by-step explanation: The area has been given as 1300 which means,
Area = L x W
1300 = L x W ———(1)
Also the perimeter has been given as 160, hence we also have
Perimeter = 2(L + W)
160 = 2(L + W)
80 = L + W ———(2)
From equation (2), make L the subject of the equation
L = 80 - W
Substitute for the value of L into equation (1)
1300 = L x W
1300 = (80 - W) x W
1300 = 80W - W^2
Rearranging the equation we now have;
W^2 - 80W + 1300 = 0
Since we cannot factorize we shall apply the quadratic equation formula to solve for W. Please refer to the attachment for details of this.
Having calculated the value of W to be either 57.32 or 22.68, we can now find the value of L as follows;
Substitute for the value of W into equation (1)
1300 = L x W
1300 = L x 57.32
Divide both sides of the equation by 57.32
22.68 = L.
(Note that if we take the other value of W which is 22.68, the value of L shall be 57.32)
Since the area of the rectangular garden must be AT LEAST 1300 square feet we shall use the exact values for;
Length = 57.32 feet
Width = 22.68 feet