If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same area as he original rectangle would result . Find the perimeter of the original rectangle .
Let x and y be the length and breadth of the rectangle respectively .
Then , `x - 4 = y + 3 or x - y = 7` .....................................(i)
Area of the rectangle = `xy`
Area of the square = `(x -4 ) (y + 3)`
`:.` ` (x - 4) (y + 3 )= xy hArr 3x - 4y = 12` ............................(ii)
Solving (i) and (ii), we get `x` = 16 and y = 9
`;.` perimeter of the rectangle = `2(x + y) ` = [2( 16 + 9)] = 50 cm.
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