if the length of a retangle is increased by 5 metres and the breadth decreased by 3 meters, the area would decrease by 5 square meters. of the length is increased by 3 metres and breadth increased by 2 meters, the area would increase by 50 square metres. What are the length and breadth?
Share
Answer:
The length is 10m
The breadth is 8m
Step-by-step explanation:
Let x be the length of the rectangle
Let y be the breadth of the rectangle
According to the question
(x+5)(y-3) = xy -5 => xy - 3x + 5y - 15 = xy - 5
(x+3)(y+2) = xy + 50 => xy + 2x + 3y + 6 = xy + 50
The final equations are,
5y - 3x - 10 = 0 (multiplying by 2)
3y + 2x - 44 = 0 (multiplying by 3)
The equations are
10y - 6x - 20 = 0
9y + 6x - 132 = 0
Using elimination method,
19y = 152
y = 152/19 = 8
6x = 132-72 = 60
x = 10
Brainliest please
Answer:
The length and breadth of the rectangle are 10 metres and 8 metres respectively.
Step-by-step-explanation:
Let the length of the rectangle be l metres.
And the breadth of rectangle be b metres.
Area of rectangle = Length * Breadth
∴ Area = lb sq.metres
From the first condition,
Length of a rectangle is increased by 5 metres and breadth is decreased by 3 metres, the area would decrease by 5 square metres.
∴ ( l + 5 ) ( b - 3 ) = ( lb - 5 )
⇒ l ( b - 3 ) + 5 ( b - 3 ) = lb - 5
⇒ lb - 3l + 5b - 15 = lb - 5
⇒ lb - 3l + 5b - lb = - 5 + 15
⇒ - 3l + 5b = 10
⇒ 3l = 5b - 10
⇒ l = ( 5b - 10 ) / 3 - - - ( 1 )
From the second condition,
Length of a rectangle is increased by 3 metres and breadth is increased by 5 metres, the area would increase by 50 square metres.
∴ ( l + 3 ) ( b + 2 ) = ( lb + 50 )
⇒ l ( b + 2 ) + 3 ( b + 2 ) = lb + 50
⇒ lb + 2l + 3b + 6 = lb + 50
⇒ lb + 2l + 3b - lb = 50 - 6
⇒ 2l + 3b = 44
⇒ [ 2 * ( 5b - 10 ) / 3 ] + 3b = 44 - - - [ From ( 1 ) ]
⇒ [ ( 10b - 20 ) / 3 ] + 3b = 44
⇒ ( 10b - 20 + 9b ) / 3 = 44
⇒ 19b - 20 = 44 * 3
⇒ 19b - 20 = 132
⇒ 19b = 132 + 50
⇒ 19b = 152
⇒ b = 152 / 19
⇒ b = 8
∴ Breadth = 8 metres
Now,
l = ( 5b - 10 ) / 3 - - - ( 1 )
⇒ l = ( 5 * 8 - 10 ) / 3
⇒ l = ( 40 - 10 ) / 3
⇒ l = 30 / 3
⇒ l = 10
∴ Length = 10 metres
∴ The length and breadth of the rectangle are 10 metres and 8 metres respectively.