Question

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.

Answer 1

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Answer 2

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