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 8 square units. if the 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 lenght and breadth of the rectangle.
Answers
Answer:
LENGTH= 344 units
BREADTH= 205 units
Step-by-step explanation:
LET THE LENGTH AND BREADTH BE 'X' AND 'Y' RESPECTIVELY.
CASE 1:
(X-5) (Y+3) = XY - 8
3X - 5Y = 7 ...............EQN-1
CASE 2:
(X-3) (Y+2) = XY + 67
2X - 3Y = 73.................EQN-2
RESOLVING EQN 1 AND EQN 2,
X = LENGTH = 344 UNITS
Y = BREADTH = 205 UNITS
Answer:
Let the length be l and breadth be b
Area of rectangle=lb
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 8 square units.
(l-5) (b+3)= lb-8
lb-5b+3l-15=lb-8
31-5b=7_ _ _ _ _ _ _ _ _ (1)
If the length is reduced by 3 units and breadth is increased by 2 units ,then the area of rectangle will increase by 67 square units.
(l-5) (b+3)=lb+67
lb-3b+2l-6=lb+67
2l-3b=73_ _ _ _ _ _ _ (2)
Multiply (1) with 2 and (2) with 3
6l-10b=14 _ _ _ _ _ _ _ _ _(3)
6l-9b=219_ _ _ _ _ _ _ _ _(4)
Subtracting from (3) - (4)
b= 205
Putting this value in (1) we get
31-5(205)=7
31=7+1025=1032
l= 344
Thus, length=344 units and breadth=205 units.