Question

If the length of a rectangle is increased by 5 metres and the breadth decreased by 3 metres, the area would decrease by 5 square metres. If the length is increased by 3 metres and the breadth increased by 2 metres, the area would increase by 50 square metres. What are the length and breadth ?

Answer 1

Let the length be x and breadth be y

1st condition :- Length increases by 5, Breadth decreases by 3, Area decreases by 5 [Area = L×B = xy ]

So, (x+5) (y-3) = xy - 5

xy + 5y - 3x - 15 = xy - 5

xy + 5y - 3x - xy = -5 + 15

-3x + 5y = 10 {equation 1}

2nd condition :- Length increases by 3, Breadth increases by 2, Area increases by 50

So, (x+3) (y+2) = xy + 50

xy + 3y + 2x + 6 = xy + 50

xy + 3y + 2x - xy = 50 - 6

2x + 3y = 44 {equation 2}

Now we have to eliminate x,

So, 2(equation 1) + 3(equation 2)

-6x + 10y = 20

+6x + 9y = 132

19y = 152

So, y = 152/19 = 8

Now, to find x, we have to put the value of y in equation 1

So, -3x + 5(8) = 10

-3x + 40 = 10

-3x = 10 - 40

-3x = -30

3x = 30

x = 30/3

x = 10

Hence, the Length of the rectangle is 10 metres and the Breadth is 8 metres.

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