The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq.cm. Find the length of the rectangle?  Answers: A) 10 cm B) 40 cm C) 20 cm D) 30 cm E) 50 cm
Let the breadth of the given rectangle be x then length is 2x.   thus area of the given rect is \fn_jvn {\color{Black} 2x^{2}}   after dec 5cm from length and inc 5cm breadth , new lenght becomes 2x-5 and breadth is x+5.thus new area =(2x-5)(x+5)=\fn_jvn {\color{Black} 2x^{2}+5x-25}   since new area is 75 units greater than original area thus   \fn_jvn {\color{Black}2x^{2}+75= 2x^{2}+5x-25}   5x=75+25   5x=100   therefore x=20   hence length of the rectangle is 40 cm.   Answer: 40 cm
<result>B</result>
The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq.cm. Find the length of the rectangle?