Question

The area of a rectangle gets reduced by 12 square units, if its length is reduced by 4 units and
breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units,
the area increases by 57 square units. Find the dimensions of the rectangle.

Answer 1

Answer:

length = 12 units

breadth = 9 units

Step-by-step explanation:

let the length be 'x' and breadth be 'y'

A = xy

A - 12 = (x - 4)(y + 3)

xy - 12 = xy + 3x - 4y -12

3x - 4y = 0

3x = 4y

A + 57 = (x + 3)(y + 2)

xy + 57 = xy + 2x + 3y +6

2x + 3y = 51

(8y/3) + 3y = 51     ( 3x = 4y )

17y = 51(3)

y = 9 units

3x = 4y

x = 12 units

hope this helps

Answer 2

Answer :

➨Length of rectangle is 12 units

➨ Breadth of rectangular is 9 units

To find :

• Dimensions of the rectangle

Solution :

• Let the length of rectangle be x
• Let the breadth of rectangle be y

By using the Area of rectangle :

• Area of rectangle = l × b
• Area of rectangle = x × y = xy

Given that, The area of rectangle gets reduced by 12 square units , if the length is reduced by 4 units and breadth is increased by 3 units so,

• Area - 12 = (length - 4) × (breadth + 3)

where, Area is xy , Length is x and breadth is y

➨ xy - 12 = (x - 4) × (y + 3)

➨ xy - 12 = x(y + 3) - 4(y + 3)

➨ xy - 12 = xy + 3x - 4y - 12

➨ 0 = xy + 3x - 4y - 12 - xy + 12

➨ 3x - 4y - 0

➨ 3x - 4y = 0 .... equation (1)

And also Given that, if we increase the length by 3 units and the breadth by 2 units, the area increases by 57 square units so,

• Area + 57 = (length + 3) × (breadth + 2)

➨ xy + 57 = (x + 3) × (y + 2)

➨ xy + 57 = x(y + 2) × 3(y + 2)

➨ xy + 57 = xy + 2x + 3y + 6

➨ 0 = xy + 2x + 3y + 6 - xy - 57

➨ 2x + 3y - 51 = 0

➨ 2x + 3y = 51 .... equation (2)

Equation are :

• 3x - 4y = 0
• 2x + 3y = 51

Now, from equation (1) :

➨ 3x - 4y = 0

➨ 3x - 4y - 0

➨ 3x = 0 + 4y

➨ x = 0 + 4y/3

Now, putting the value of x in equation (2) we get,

➨ 2x + 3y = 51

➨2(0 + 4y/3) + 3y = 51

Now multiplying both sides by 3 we get,

➨ 3 × 2(0 + 4y/3) + 3 × 3y = 51 × 3

➨ 2(0 + 4y) + 9y = 153

➨ 0 + 8y + 9y = 153

➨ 17y = 153 - 0

➨ 17y = 153

➨ y = 153/17

➨ y = 9

Now , putting the value of y = 9 in equation (1) we get,

➨ 3x - 4y = 0

➨ 3x - 4(9) = 0

➨ 3x - 36 = 0

➨ x = 36/3

➨ x = 12

So here ,

• x = 12
• y = 9

Hence ,

➨ Length of rectangle is 12 units

➨ Breadth of rectangular is 9 units