<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>&lt;p&gt;Let the length of a square be &amp;lsquo;a&amp;rsquo;.&lt;/p&gt; &lt;p&gt;And the radius of a circle be &amp;lsquo;r&amp;rsquo;.&lt;/p&gt; &lt;p&gt;Now, a = 2r ----- (i)&lt;/p&gt; &lt;p&gt;Perimeter of the rectangle = 1/2 &amp;times; 4a = 2a&lt;/p&gt; &lt;p&gt;=&amp;gt; 2(l + b) = 2a&lt;/p&gt; &lt;p&gt;=&amp;gt; 2 &amp;times; 16 = 2a&lt;/p&gt; &lt;p&gt;=&amp;gt; a = 16 cm&lt;/p&gt; &lt;p&gt;Putting value of &amp;lsquo;a&amp;rsquo; in (i) we get,&lt;/p&gt; &lt;p&gt;Radius = r = 16/2 = 8 cm&lt;/p&gt; &lt;p&gt;Area of the circle = &amp;pi;r&lt;sup&gt;2&lt;/sup&gt;&amp;nbsp;= 2 &amp;times; 8 &amp;times; 8 = 128 cm&lt;sup&gt;2&lt;/sup&gt;.&lt;/p&gt;</p>