High School

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55. The length of a rectangle exceeds twice its breadth by 3 metres. If its perimeter is 246 metres, then the breadth is:

(A) 40 metres
(B) 60 metres
(C) 80 metres
(D) 83 metres

Answer :

To solve the problem of finding the breadth of the rectangle, we can use algebra to set up equations based on the information given.

Let:

  • [tex]b[/tex] be the breadth (width) of the rectangle.
  • [tex]l[/tex] be the length of the rectangle.

From the problem statement, we know:

  1. The length exceeds twice the breadth by 3 metres. This translates to the equation:
    [tex]l = 2b + 3[/tex]

  2. The perimeter of the rectangle is 246 metres. The perimeter [tex]P[/tex] of a rectangle can be calculated using the formula:
    [tex]P = 2(l + b)[/tex]
    Given that the perimeter is 246 metres, we have:
    [tex]2(l + b) = 246[/tex]

Let's solve these equations step-by-step:

From the perimeter equation:
[tex]2(l + b) = 246[/tex]
[tex]l + b = 123[/tex]

Substitute the expression for [tex]l[/tex] from the first equation into this equation:
[tex]2b + 3 + b = 123[/tex]
Simplify:
[tex]3b + 3 = 123[/tex]
Subtract 3 from both sides:
[tex]3b = 120[/tex]
Divide by 3:
[tex]b = 40[/tex]

So, the breadth of the rectangle is [tex]40[/tex] metres.

The correct option is (A) 40 metres.

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