The perimeter of a rectangular field is 44m and it's area is 120m². Find the length and breadth of the field.
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Answer:
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.
{ Doesn't really matter because I had not defined which one is length and breadth in “a” and “b” and so their values are interchangeable }
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.
Which is our answer.
Let length is x cm and bredth is y cm of a rectangle , Acordingly:-
2(x+y)= 44 or x+y =22…………(1)
x×y = 120…………………….(2)
From eq.(1) put y= 22-x
x×(22-x)= 120
or 22x - x^2 = 120
or x^2 -22x +120 =0
or (x-12) (x-10) =0
or x = 12 cm or 10 cm .
But y =22-x
y = 22 -12 =10 or 22–10 =12.
Length = 12cm or 10 cm
bredth = 10 cm or 12 cm . Answer.
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