the area of a rectangular field is 500 metres square . if the length is reduced by 3 metres and bredth is increased by 2 metres then it forms a square. find the length and breadth of the rectangle field.
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kaushikmishra09:
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Answer:
Step-by-step explanation:
Let l be the length of rectangle and b be the breadth
Area of rectangle = 500 m^2
lb = 500
b = 500/l --------(i)
If l is reduced by 3 and b increased by 2 then rectangle becomes a square
Since sides of a square are equal
l - 3 = b + 2
l - b = 5
Substituting value of b from eqn (i)
l - 500/l = 5
l^2 - 500 = 5l
l^2 - 5l - 500 = 0
l^2 - 25l + 20l - 500 = 0
l(l -25) + 20(l - 25) = 0
(l + 20)(l - 25) = 0
l = -20 or l = 25
Length cannot be negative
Therefore , length = 25 m
breadth = 500/l
= 500/25
= 20 m
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