The area of a rectangle is reduced by 67 square metres, when its length is increased by 3 metres and breadth decreased by 4 metres. If the length is decreased by 1 metre and breadth is increased by 4 metres, the area is increased by 89 square metres. Find the dimensions of the rectangle.
Answers
Answer:
Step-by-step explanation:
Let the length of the rectangle be x metres and the breadth be y metres.
Area of the rectangle=length×breadth
=x×y=xy sq. metres
From the given information, we have,
(x+3)×(y−4)=xy−67
and(x−1)×(y+4)=xy+89
(x+3)×(y−4)=xy−67
=>xy−4x+3y−12=xy−67
=>4x−3y=55
=>4x=3y+55....(i)
Also,(x−1)×(y+4)=xy+89
=>xy+4x−y−4=xy+89
=>4x−y=93....(ii)
Substituting equation (i) in equation (ii), we get,
4x−y=93
=>3y+55−y=93
=>2y=38
=>y=19
Substituting y=19 in equation (i), we get,
4x=3y+55
=>4x=3(19)+55
=>4x=112
=>x=28
Therefore, length of rectangle =x=28 metres
breadth of rectangle =y=19 metres=>2y=38
=>y=19
Substituting y=19 in equation (i), we get,
4x=3y+55
=>4x=3(19)+55
=>4x=112
=>x=28
Therefore, length of rectangle =x=28 metres
breadth of rectangle =y=19 metres
Answer:
Here is the correct answer
