One side of a rectangle is 3 cm shorter than the other side. If we increase the length of each side by 1 cm, then the area of the rectangle will increase by 22 cm2. Find the lengths of all sides.	Choose the most appropriate option: A) 10 and 3 B) 7 and 10 C) 10 and 7 D) 3 and 10 E) 12 and 9
Let x be the length of the longer side x&gt;3, then the other side's length is x−3 cm. Then the area is S1 = x(x - 3) cm2. After we increase the lengths of the sides they will become (x+1) and (x−3+1)=(x−2) cm long. Hence the area of the new rectangle will be A2=(x+1)⋅(x−2) cm2, which is 22 cm2 more than the first area. Therefore   A1+22=A2   x(x−3)+22=(x+1)(x−2)   x2−3x+22=x2+x−2x−2   2x=24   x=12. So, the sides of the rectangle are 12 cm and (12−3)=9 cm long.   So answer is 12 and 9.
<result>E</result>
One side of a rectangle is 3 cm shorter than the other side. If we increase the length of each side by 1 cm, then the area of the rectangle will increase by 22 cm2. Find the lengths of all sides.