Question

The area of a rectangle gets reduced by 9 m2 if its length is reduced by 5 m and breath is increased by 3 m. If we increased the length by 3 m and breath by 2 m, the area is increased by 67 m2. The length of the rectangle is:

Answer 1

Let the length and breadth of a rectangle be x and y respectively.
Area of rectangle = L X B = xy. m^2
CASE I : when length is reduced by 5 m then
New length = ( x - 5 )
And, when breadth is increased by 3 m then
New breadth = ( y + 3 ) m
====> New Area = ( xy - 9 ) m^2
( x - 5 ) ( y + 3 ) = xy - 9
xy + 3x - 5y - 15 = xy - 9
3x - 5y - 15 = - 9
3x - 5y = 6 ...................(i)
CASE II : When length is increased by 3 m then
New length = ( x + 3 ) m
And, when breadth is increased by 2 m then
New breadth = ( y + 2 ) m
====> New Area = ( xy + 67 ) m^2
( x + 3 ) ( y + 2 ) = xy + 67
2x + 3y = 61 ....................(ii)
Now, Multiply eq. (i) by 3 and eq. (ii) by 5. Then,
9x - 15y = 18 ....................(iii)
10x + 15y = 305 . ................(iv)
By adding eq. (iii) and (iv). We get,
19x = 323
x = 17 m ........Answer
Hence, The length of rectangle is 17 m.