<em>Since, the area of the rectangular base = </em>
<em />
<em>We have to determine the width if length is (3x+1)</em>
<em />
<em>Let us split the middle terms of the given equation to find its factors.</em>
<em />
<em />
<em />
<em>Taking common from first, second and third, fourth terms.</em>
<em />
<em>= 3x(4x-5)+1(4x-5)</em>
<em />
<em>= (3x+1) (4x-5)</em>
<em />
<em>Since, (3x+1) is the length of the rectangular base.</em>
<em />
<em>Therefore, the width of the rectangular base is (4x-5) units.</em>
<em />
<em>Now, Volume of the rectangular prism is given by the polynomial</em>
<em />
<em />
<em />
<em>We have to find width and height.</em>
<em />
<em>Let x = - in the given equation of volume.</em>
<em />
<em>We get as, </em>
<em />
<em>-135+135=0</em>
<em />
<em>Hence, (3x+1) is a factor of the given volume polynomial.</em>
<em />
<em>Now, performing long division of the given polynomial by (3x+1),</em>
<em />
<em>we get factors as (4x-5) and (2x-3).</em>
<em />
<em><u>So, the width is (4x-5) units and height is (2x-3) units.</u></em>
