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..if the length of a rectangle is reduced by 5 units and its breadth is increased by 3 units then the area of the rectangle is reduced by 9 square units if length is reduced by 3 units and breadth is increased by 2 units then the area of rectangle will increase by 67 square units then find the length and breadth of the rectangle
Answers
Answer:
Length = 347
Breadth = 207
Step-by-step explanation:
Let Say Length of rectangle = L
Breadth of Rectangle = B
Area of rectangle = length * Breadth = LB
Length reduced by 5 so new length = L-5
Breadth increased by 3 so new breadth = B + 3
New Area = (L-5)(B+3) = LB + 3L - 5B - 15
New area = Old area - 9
LB + 3L -5B - 15 = LB - 9
=> 3L - 5B = 6 Eq 1
Length Reduced by 3 = L-3
Breadth increased by 2 = B + 2
Area = (L-3)(B+2) = LB + 2L - 3B - 6
Area = Old area + 67
LB + 2L -3B -6 = LB + 67
=> 2L - 3B = 73 - Eq2
Eq1 *2 - Eq2 *3
6L - 10B - 6L + 9B = 12 - 219
=> -B = - 207
=> B = 207
2L - 3B = 73
2L - 3*207 = 73
2L = 73 + 621
L = 347
Length = 347
Breadth = 207
Answer:
347, 207
Step-by-step explanation:
Let the length of the rectangle be 'x' and breadth be 'y'.
(i)
Area of the rectangle is reduced by 9 units.
Area = xy - 9.
Length is reduced by 5 units and breadth is increased by 3 units.
Length = x - 5.
Breadth = y + 3.
So, Area = (x - 5)(y + 3)
⇒ xy - 9 = xy + 3x - 5y - 15
⇒ 3x - 5y = 6
(ii)
Area of the rectangle will increase by 67 sq.units.
Area = xy + 67.
Length is reduced by 3 units and breadth is increased by 2 units.
Length = x - 3.
Breadth = y + 2.
So, Area = (x - 3)(y + 2)
⇒ xy + 67 = (x - 3)(y + 2)
⇒ xy + 67 = xy + 2x - 3y - 6
⇒ xy + 67 - xy - 2x + 3y + 6 = 0
⇒ -2x + 3y + 73 = 0
⇒ 2x - 3y - 73 = 0
⇒ 2x - 3y = 73
On solving (i) * 2 & (ii) * 3, we get
6x - 10y = 12
6x - 9y = 219
------------------------
-y = -207
y = 207
Substitute y = 207, we get
6x - 10y = 12
6x - 10(207) = 12
6x - 2070 = 12
6x = 2082
x = 347.
Therefore:
Length of the rectangle = 347.
Breadth of the rectangle = 207.