Question : The breadth of a rectangle is $\frac{4}{5}$th of the radius of a circle. The radius of the circle is $\frac{1}{5}$ of the side of a square, whose area is 625 cm2. What is the area of the rectangle if the length of the rectangle is 20 cm?
Option 1: 150 cm2
Option 2: 600 cm2
Option 3: 100 cm2
Option 4: 80 cm2
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Correct Answer: 80 cm 2
Solution : The breadth of a rectangle is $\frac{4}{5}$ of the radius of a circle The radius of the circle is $\frac{1}{5}$ of the side of a square, whose area is 625 cm$^2$ The length of the rectangle is = 20 cm Formula Used: The area of the square = $a^2$ The area of the rectangle = $l \times b$ Calculations: According to the question, The breadth of a rectangle (b) is $\frac{4}{5}$ of the radius of a circle (r) ⇒ $b = \frac{4}{5}\times r$ The radius of the circle (r) is $\frac{1}{5}$ of the side of a square (a) ⇒ $r= \frac{1}{5} \times a$ The area of square = $a^2$ $625 = a^2$ ⇒ $a = 25$ cm The radius of the circle will be = $\frac{1}{5}\times a$ = $\frac{1}{5}\times 25$ = 5 cm The breadth of the rectangle will be $b = \frac{4}{5}\times r$ $b = \frac{4}{5}\times 5$ = 4 cm The area of the rectangle will be = $l \times b$ = 20 × 4 = 80 cm$^2$ Hence the correct answer is 80 cm$^2$.
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