A rectangle has the same area as another, whose length is 6 m more and breadth
IS 4 m less. It has also the same area as the third, whose length is 8 m more and
breadth 5 m less. Find the length and breadth of the original rectangle.
Answers
Answered by
6
The length of the original rectangle is 24 m and breath is 20 m
LET THE AREA OF THE THREE RECTANGLE = A
ACCORDING TO THE GIVEN CONDITION
AREA OF ORIGINAL RECTANGLE =A= XY
AREA OF ORIGINAL RECTANGLE=A=(X+6)*(Y-4)
AREA OF ORIGINAL RECTANGLE=A=(X+8)*(Y-5)
(X+6)*(Y-4)=XY
XY + -4X+ 6Y-24 =XY
4X-6Y= -24 --eq1
(X+8)*(Y-5)= XY
XY -5X+8Y -40 =XY
5X -8Y=-40 eq2
solving eq1 and eq2 simultaneously
[4X-6Y= 24]*5 20X -30Y=120 ; 20X =-120 + 30Y
[5X -8Y=40 ]*4 20X - 32Y = -160 ; 20X =- 160 + 32Y
THEREFORE,
-120 + 30Y = - 160 + 32Y
2Y= 40
Y= 20 m
By eq2 we 5x=8y -40
5X= 160-40
X=120/5= 24m
therefore length of the original rectangle is X =24m
and breath of the original rectangle is Y =20m
Similar questions