<PRE><B>Question 1209976</B>
&lt;pre&gt;
1.A rectangle 9cm long is equal in area to a spuare which has a perimeter of 24cm. Find the width of the rectangle.
2.find the length of the side of a square that is equal in area to a rectangle measuring 45cm by 5cm.
 I will be glad if you could help solve

&lt;font color = red&gt;&lt;font size = 4&gt;&lt;b&gt;1.&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;  With perimeter of square being 24 cm, length of 1 side of square = {{{24/4}}} = 6 cm
    As such, area of square = 6 * 6  = 6&lt;sup&gt;2&lt;/sup&gt; = 36 sq cm 

    Let width of rectangle be W
    With length of rectangle being 9 cm, and its area being the same as square&#39;s
    area (36 sq cm), we get:  LW = 6&lt;sup&gt;2&lt;/sup&gt;
                              9W = 36
    &lt;font color = red&gt;&lt;font size = 4&gt;&lt;b&gt;Width of rectangle&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;, or W = {{{36/9}}} = &lt;font color = red&gt;&lt;font size = 4&gt;&lt;b&gt;4 cm&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;

&lt;font color = red&gt;&lt;font size = 4&gt;&lt;b&gt;2.&lt;/font&gt;&lt;/font&gt;&lt;/b&gt; Rectangle’s dimensions: 45 cm by 5 cm, so area = 45(5) = 225 sq cm
    With length of 1 side of square being S, area of square = S&lt;sup&gt;2&lt;/sup&gt; 
    Since areas of square and rectangle are the same, S&lt;sup&gt;2&lt;/sup&gt; = 225
    &lt;font color = red&gt;&lt;font size = 4&gt;&lt;b&gt;Length of 1 side of the square&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;, or S = {{{sqrt(225)}}} = &lt;font color = red&gt;&lt;font size = 4&gt;&lt;b&gt;15 cm&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;&lt;/pre&gt;</PRE>