Maths Puzzles With Answers #40

Solution:-



Let x be the length of the longer side x>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 18 cm² more than the first area. Therefore     


                           A1+18= A2

                               x(x−3)+18=(x+1)(x−2)

                      x2−3x+18= x2+x−2x−2

                     2x=20

                    
${\displaystyle x=10}$. So, the sides of the rectangle are ${\displaystyle \mathrm{<span\; style="color:\; red;\; font-size:\; large;"><b>10</b></span>}}$ cm and (${\displaystyle \mathrm{<span\; style="font-size:\; 15.6px;">10</span>}<span\; style="font-size:\; 15.6px;">-</span>\mathrm{<span\; style="font-size:\; 15.6px;">3</span>}<span\; style="font-size:\; 15.6px;">)</span><span\; style="font-size:\; 15.6px;">=</span>\mathrm{<span\; style="color:\; red;\; font-size:\; large;"><b>7</b></span>}}$ cm long.