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
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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