The breadth of a rectangle is 4/5 of the radius of a circle. The radius of the circle is 1/5 of the side of a square, whose area is 625 cm2. What is the area of the rectangle if the length of a rectangle is 20 cm?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 80 cm2
Given, the radius of the circle is 1/5 of the side of a square, whose area is 625 cm2. So, the area of the square is:
Side of the square = 5 × radius of the circle
= 5 × (1/5) × side of the square (since the radius is 1/5 of the side of the square)
= side of the square
Therefore, the side of the square = √625 = 25 cm.
Now, the radius of the circle is 1/5 of the side of the square, which is 25 cm/5 = 5 cm.
Hence, the breadth of the rectangle is 4/5 of the radius of the circle, which is (4/5) × 5 cm = 4 cm.
Given, the length of the rectangle is 20 cm.
Therefore, the area of the rectangle is:
Area of rectangle = length × breadth
= 20 cm × 4 cm
= 80 cm2