The area of a rectangle gets reduced by 9 square metres, if it's length is reduced by 5 metres and breadth is increased by 3 metres. If we increase the length by 3 metres and the breadth by 2 metres ,the area increases by 67 square metres . Find the length and breadth of the rectangle
Answers
Answer:
x=17 units
y=9 units
Step-by-step explanation:
let the x with the length and y with the breadth of rectangle
therefore area of rectangle = xy
(x - 5 )(y + 3)= x y - 9.........1
(x + 3) ( y+ 2)= x y + 67........2
first equation
x(y + 3) -5(y + 3)= xy -9
3x -5 y - 15 + 9 = 0
3x -5 y - 6 = 0..........3
solving second equation
(x + 3) (y + 2)= xy + 67
x y + 2x + 3 y + 6 = xy + 67
2x + 3 y + 6 -67=0
2 x + 3 y -61 = 0
multiplying equation 3 by 3 and 4 by 5
3x-5y-6=0.......3...*3
2x+ 3 y - 61 = 0.......*5
adding a question 3 and 4 we get
9x-15y=18
10x+15y=305
___________
19x. =323
x=323/19
x=17 units
putting the value of x in equation 4
2 x + 3 y = 61
2 *17 + 3 y = 61
34 + 3 y = 61
3 y = 61 - 34
3 y = 27
y = 27 / 3
y = 9 units
therefore x = 17 units
and y = 9 units
Step-by-step explanation:
Let the length of the rectangle be x m and the breadth of the rectangle be y m.
Then,
Area of rectangle = xy m²
★ If its length is reduced by 5 m and breadth is increased by 3 m,
Then,
Length = (x-5) m
Breadth = (y+3) m
A/Q, [ 1st case]
(x-5)(y+3)=xy-9
→ xy+3x-5y-15=xy-9
→ 3x-5y=15-9
→ 3x-5y = 6 .................... [ equation 1 ] ×2
★ If the length is increased by 3 m and the breadth is increased by 2 m,
Then,
Length = (x+3) m
Breadth = (y+2) m
A/Q, [ 2nd case]
(x+3)(y+2) = xy+67
→ xy +2x + 3y +6 = xy + 67
→ 2x+3y = 61................... [ equation 2] × 3
Now,
2 equations will be,
6x -10y = 12..........[1]
6x + 9y = 183.........[2]
Now subtract eq (1) from eq(2).
6x+9y-6x+10y = 183-12
→ 19y = 171
→ y = 9
Breadth = 9 m
Now out y=9 in eq(1).
3x-5y=6
→ 3x - 5×9 = 6
→ 3x = 6+45
→ x = 17
Length = 17 m