Answer:
Dimension => 10 m × 9.6 m
Explanation:
From the question given above, the following data were obtained:
Area (A) = 96 m²
Circumference (C) = 39.2 m
Dimension =.?
Next, we shall determine the Lenght and breadth of the rectangle. This can be obtained as follow:
Let L be the Lenght
Let B be the breadth
Area of a rectangle = L × B
96 = L × B ..... (1)
Circumference of rectangle = 2(L + B)
39.2 = 2(L + B) .... (2)
From equation 2, make L the subject
39.2 = 2(L + B)
Divide both side by 2
39.2 /2 = L + B
19.6 = L + B
Rearrange
L = 19.6 – B ....(3)
Substitute the value of L in equation 3 into equation 1
96 = L × B
L = 19.6 – B
96 = (19.6 – B ) × B
Clear bracket
96 = 19.6B – B²
Rearrange
B² – 19.6B + 96 = 0
Solving by factorisation
B² – 10B – 9.6B + 96 = 0
B(B – 10) – 9.6(B – 10) = 0
(B – 9.6)(B – 10) = 0
B – 9.6 = 0 or B – 10 = 0
B = 9.6 or B = 10
Substitute the value of B into equation 3:
L = 19.6 – B
B = 9.6
L = 19.6 – 9.6
L = 10
Or
L = 19.6 – B
B = 10
L = 19.6 – 10
L = 9.6
Since the length is always longer than the breadth,
Length (L) = 10 m
Breadth (B) = 9.6 m
Finally, we shall determine the dimension of the rectangle. This can be obtained as follow:
Length (L) = 10 m
Breadth (B) = 9.6 m
Dimension =?
Dimension = L × B
Dimension = 10 m × 9.6 m