area related problems

Question

Area of square is 500 square cm it is converted to rectangle by increasing the length by 5 cm without changing the perimeter .then what change made to the area

Answer 1

Side of square, a=sqrt(500). Perimeter=4a. Perimeter of rectangle=4a=2(a+5)+2x, where x is the width. So 4a-2a-10=2x, so x=a-5 (as you would expect!) and the area=

(a-5)(a+5)=a^2-25=500-25=475 sq cm.