Question : The area of a square and rectangle are equal. The length of the rectangle is greater than the length of a side of the square by 10 cm and the breadth is less than 5 cm. The perimeter (in cm) of the rectangle is:
Option 1: 50
Option 2: 40
Option 3: 80
Option 4: 100
Correct Answer: 50
Solution : Let $a$ be the side of the square and $l,b$ be the length and breadth of a rectangle. $l = a + 10$ $b = a - 5$ Area of square = area of rectangle $⇒a^2 = lb$ $⇒a^2 = (a+10)(a-5)$ $⇒a^2 = a^2 + 10a -5a -50$ $⇒5a =50$ $\therefore a=10$ So, $l = 10 +10 = 20$ $b = 10 - 5 = 5$ Perimeter of a rectangle = $2(l+b)= 2 × (20+5)= 2 × 25= 50$ cm Hence, the correct answer is 50.
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