In a rectangle if length is increased by 7 units & breadth is decreased by 3 units or if length is decreased by 7 units & breadth is increased by 5 units, in both the cases the area remains same. Find the dimensions of the rectangle. Also find the area of the rectangl
Answers
length =28 bregth=15
Step-by-step explanation:
first let us consider length as "X"and bregth as"y"
given that if X is increased by 7 units and y is decreased by3 units
and area remains same so we know the area of a rectangle is is length x breath could also be returned in terms of X and y i.e. xy
we get the equation now
(X+7)(y-3)=xy as given that area does not changes
now simplifying it
xy-3x+7y-21= xy
7y-3x-21=xy-xy
7y-3x-21=0 ................(i)
also also given that if length is decreased by 7 units and breadth is increased by 5 units the area remain samehence in terms of X and y would be written as
(x-7)(y+5)=xy
xy-7y+5x-35=xy
-7y+5x-35=xy-xy
-7y+5x-35=0........................(ii)
adding equation i and ii
7y-3x-21=0
-7y+5x-35=0
________________
0+2x-56=0
2x=56
X=28
putting X in ii
we get y = 15