Question

The length of a rectangle is twice its breadth. On increasing both the length and the breadth by four units the perimeter of the new rectangle became thrice the perimeter of the original rectangle. find the dimensions of the original rectangle.​

Answer 1

The length of a rectangle is twice it's breadth.

• Breadth = x units
• Length = 2x units

We know that the :

• Perimeter of rectangle = 2 (L + B)

So the perimeter will be :

• P = 2 (2x + x) units
• P = 2 (3x) units
• P = 6x units

Therefore the perimeter of the rectangle is 6x units originally.

On increasing both the length and breadth by four units, the perimeter of the new rectangle became thrice the perimeter of the original rectangle :

• 2 (L + 4 + B + 4) = 3 (Original perimeter)
• 2 (x + 4 + 2x + 4) = 3 (6x)
• 2 (3x + 8) = 18x . . . . . . (1)
• 6x + 16 = 18x
• 6x - 18x = - 16
• - 12x = - 16
• x = - 16/- 12
• x = 4/3

Therefore the value of x is 4/3.

Finding the dimensions :

★ Breadth :

• B = x units
• B = 4/3 units

★ Length :

• L = 2x units
• L = 2 (4/3)
• L = 8/3 units

Therefore, the original length and breadth of the rectangle are 8/3 and 4/3 units.

V E R I F I C A T I O N :

From (1), we know that :

• 2 (3x + 8) = 18x
• 2 [3(4/3) + 8] = 18 (4/3)
• 2 (4 + 8) = 6 (4)
• 2 (12) = 24
• 24 = 24
• LHS = RHS

H E N C E , V E R I F I E D !