a rectangle has the same area as another whose length is 6 m more and breadth is 4m less it has also the same area as the third whose length is 8m more and Breadth 5m less find the lengthy and breadth of the original rectangle
Answers
Answer:
length is 28 and breath is 20
Step-by-step explanation:
Let , Lenght be x and Breath be y
Area of Rectangle = length × breath
= xy
According to the first condition ,
xy = ( x + 6) ( y - 4 )
xy = xy - 4x + 6y - 24
xy - xy = - 4x + 6y - 24
- 4x + 6y = 24
4x - 6y = ( - 24 )
Dividing by 2 both side ,
2x - 3y = ( - 12 ) ......... 1st equation
According the the second condition ,
xy = ( x + 8 ) ( y - 5 )
xy = xy - 5x + 8y - 40
xy - xy = - 5x + 8y - 40
- 5x + 8y = 40
5x - 8y = ( - 40 ) .......... 2nd equation
Multiply equation ( 1 ) by 5
10x - 15y = ( - 60 ) ........ 3rd equation
Multiply equation ( 2 ) by 2
10x - 16y = ( - 80 ) ....... 4th equation
Subratct equation ( 3 ) From ( 4 )
10x - 16y = - 80
10x - 15y = - 60
_________________
- y = - 20
y = 20
put value of y in equation 3rd
10x - 15 ( 20 ) = - 20
10x - 300 = - 20
10x = - 20 + 300
10x = 280
x = 280 ÷ 10
x = 28
therefore , length of rectangle is 28 and breath is 20
Answer:
Step-by-step explanation:
