The perimeter of a square is one-fourth of the perimeter of a Rectangle. If the perimeter of the square is 44 cm, and the length of the Rectangle is 51 cm, what is the difference between the breadth of the Rectangle and the side of the square?
Solution
Correct Answer: Option C
We know that, formulae:
⇒ Perimeter of a square = 4 × side of square,
⇒ Perimeter of a rectangle = Sum of all the sides.
Let side of the square be ‘a’ and sides of the rectangle be ‘l’ and ‘b’,
According to the question
\(\Rightarrow 4a = \frac{1}{4} \times 2\left( {l + b} \right)\)
\(\Rightarrow 44 = \frac{1}{4} \times 2\left( {l + b} \right)\)
\(\Rightarrow 44 = \frac{1}{4} \times 2\left( {51 + b} \right)\)
\(\Rightarrow \frac{{44 \times 4}}{2} - 51 = b\)
⇒ b = 37.
∴ Side of square = (44/4) =11
∴ Required difference = 37 – 11 = 26.
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