The area of a rectangular is reduced to 9 square unit, If its length is reduced by 5 unit and breath is increased by 3 unit. If we we increase the length by 3 unit and the breath by two unit , the new area increase by 67 square unit. Find the length and breath.
Answers
Let the length of the rectangle be x and breadth be y.
» Case 1st
Area of Rectangle = Length × Breadth
️ = (xy) unit
New length = (x - 5) units
New breadth = (y + 3) units
Area = (xy - 9) sq units.
A.T.Q.
Area = l × b
(l × b) = xy - 9
(x - 5) (y + 3) = xy - 9
xy + 3x - 5y - 15 = xy - 9
xy + 3x - 5y - xy = - 9 + 15
3x - 5y = 6 ______ (eq 1)
» Case 2nd.
New length = (x + 3) units
New breadth = (y + 2) units
New Area = (xy + 67) sq units
A.T.Q.
Area = l × b
(x + 3)(y + 2) = xy + 67
xy + 2x + 3y + 6 = xy + 67
xy + 2x + 3y - xy = 67 - 6
2x + 3y = 61 ________ (eq 2)
______________________________
• Multiply (eq 1) with 2 and (eq 2) with 3
3x - 5y = 6 (× 2)
=> 6x - 10y = 12 ______ (eq 3)
2x + 3y = 61 (× 3)
=> 6x + 9y = 183 _______ (eq 4)
______________________________
Subtract (eq 3) from (eq 4)
=> 6x + 9y - (6x - 10y) = 183 - 12
=> 6x + 9y - 6x + 10y = 171
=> 19y = 171
=> y = 9
• Put value of y in (eq 1)
=> 3x - 5(9) = 6
=> 3x - 45 = 6
=> 3x = 51
=> x = 17
_____________________________
Length of rectangle = 17 units
Breadth of rectangle = 9 units.
___________ [ANSWER]