question_answer

  Perimeter of a square and a rectangle is same. If a side of the square is 15 cm and one side of the rectangle is 18 cm. Find the area of the rectangle.

Answer:

Given, a side of a square =15 cm We know that, the perimeter of a square \[=4\times \] Side of a square \[=4\times 15\text{ }cm=60\text{ }cm\] Here, Length of a rectangle = 18 cm                                                                                             \[\therefore \] Perimeter of a rectangle \[=2\times \] (Length + Breadth) = 2 (18 + Breadth) According to the question, Perimeter of a square = Perimeter of a rectangle \[\therefore \]      60 = 2 (18 + Breadth)                                                                                                    \[\frac{60}{2}=\] (18 + Breadth) \[\Rightarrow \]   18 + Breadth = 30 \[\therefore \]               Breadth = 30 - 18 = 12 cm                                                                                                Now, area of the rectangle = Length \[\times \] Breadth             \[=18\times 12=216\text{ }sq.\text{ }cm\] Hence, the area of the rectangle is 216 sq cm.