the perimeter of a rectangular field is 44 metre and its area is 120 metre square find the length and breadth of the field
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Step-by-step explanation:
Let the sides of our rectangle be “a” and “b”.
The perimeter of a triangle = sum of the lengths of its side = 2a + 2b.
Area of a rectangle = length * breadth
= ab.
Perimeter = 2a + 2b = 44. Which implies that,
a + b = 22.
Area = ab = 120.
And we know,
(a - b)^2 = (a + b)^2 - 4ab
From this if we calculate the value of a - b, we can figure out the value of “a” and “b”.
(a - b)^2 = (22)^2 - 4*120
= 484 - 480 = 4.
Which implies that,
a - b = 2, or a - b = - 2.
And we had found out before that,
a + b = 22, through our perimeter.
If we solve these two equations, we get,
a = 12, b = 10.
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