A wire of length 86 cm is bent in the form of a rectangle such that its length is 7 cm more than its breadth. Find the length and the breadth of the rectangle so formed.

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Solution

Let the breadth of the rectangle be x cm.
Then, the length of the rectangle will be (x + 7) cm.
Perimeter of the rectangle = 2(Length + Breadth) = 2( x + 7 + x) cm
Given perimeter of the rectangle = Length of the wire = 86 cm

∴ 2( x + 7 + x) = 86
or, 2 ( 2x + 7 ) = 86
or, 2 ×2x + 2 × 7 = 86 [On expanding the brackets]
or, 4x + 14 = 86
or, 4x + 14 - 14 = 86 - 14 [Subtracting 14 from both the sides]
or, 4x = 72
or, $\frac{4 x}{4} = \frac{72}{4}$ [Dividing by 4 on both the sides]
or, x = 18 metres
Breadth of the hall = x
= 18 metres
Length of the hall = x + 7
= 18 + 7
= 25 metres

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