Question
<p>&lt;p&gt;The length of sides of a
square is twice the radius of a circle and perimeter of a rectangle is half the perimeter of the square. If the sum of length and breadth of rectangle is 16 cm, then find the area of the circle (in cm&lt;sup&gt;2&lt;/sup&gt;). [Take &amp;pi; = 2]&lt;/p&gt;</p>Solution
<p><p>Let the length of a square be &lsquo;a&rsquo;.</p> <p>And the radius of a circle be &lsquo;r&rsquo;.</p> <p>Now, a = 2r ----- (i)</p> <p>Perimeter of the rectangle = 1/2 &times; 4a = 2a</p> <p>=&gt; 2(l + b) = 2a</p> <p>=&gt; 2 &times; 16 = 2a</p> <p>=&gt; a = 16 cm</p> <p>Putting value of &lsquo;a&rsquo; in (i) we get,</p> <p>Radius = r = 16/2 = 8 cm</p> <p>Area of the circle = &pi;r<sup>2</sup>&nbsp;= 2 &times; 8 &times; 8 = 128 cm<sup>2</sup>.</p></p>
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