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 24 cm2. Find the lengths of all sides. Choose the correct option:
A) 10 and 3  B) 7 and 10  C) 10 and 7  D) 3 and 10  E) 13 and 10
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 24 cm2 more than the first area. Therefore   A1+24=A2   x(x−3)+24=(x+1)(x−2)   x2−3x+24=x2+x−2x−2   2x=26   x=13. So, the sides of the rectangle are 13 cm and (13−3)=10 cm long.   So answer is 13 and 10.
<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 24 cm2. Find the lengths of all sides.