The area of a square is $ 4096 ext{ sq cm}$. Find the ratio of the breadth and the length of a rectangle who

Question

The area of a square is $ 4096 	ext{ sq cm}$. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is $ 24 	ext{ cm}$ less than the side of the square.

Examoogle · Accepted Answer

The correct answer is Option A: 5 : 16. Calculate side $s = \sqrt{4096} = 64$. Then $breadth = 64 - 24 = 40$ and $length = 2 	imes 64 = 128$. Ratio = $40:128 = 5:16$.

Step-by-Step Solution & Concepts:
Shortcut Trick: Calculate side $s = \sqrt{4096} = 64$. Then $breadth = 64 - 24 = 40$ and $length = 2 	imes 64 = 128$. Ratio = $40:128 = 5:16$.

Formula Used: $$Area_{square} = side^2, Ratio = \frac{breadth}{length}$$

Given: Area of a square = 4096 sq cm. Rectangle length = 2 × side of square. Rectangle breadth = (side of square - 24) cm.

Steps: Calculate the side of the square: The area of a square is given as $4096$ sq cm. Using the formula $Area = s^2$, we find $s = \sqrt{4096}$.. Determine rectangle dimensions: The length $L$ of the rectangle is twice the side of the square, and the breadth $B$ is $24$ cm less than the side.. Calculate the ratio: The ratio of breadth to length is $B : L$. Dividing both terms by their greatest common divisor ($8$):

Answer: A is correct because the calculated ratio of breadth (40) to length (128) simplifies to 5:16.

Exam Tip: This type of dimension-based ratio problem frequently appears in arithmetic sections to test basic algebraic manipulation along with geometric properties.

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