The perimeter of an rectangle is 90m. If the length is increased by 3m and breath is decreased by 4m. Then area is decreased by 52m ^2. Find the original dimension of the rectangle.
Answers
Answer:
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
Answer:
l=23m
b=22m
Step-by-step explanation:
given,perimeter = 90m
l = x-3m
b= x-4m
since , perimeter of a rectangle = 2 (l+b)
implies,90m= 2 ( x-3 + x- 4)
implies , 90m = 2 × (2x - 7)
implies , 90m = 4x - 14
implies , 90 + 14 = 4x
imp. 104 = 4x
imp. x = 104
____
4
imp. x = 26
now , the dimensions are :
length = ( x - 3)= (26 - 3)
= 23m
breadth = (x - 4) = (26 - 4)
= 22m