question_answer

The side of a square is 5 cm. How many times does the area increase, if the side of the square is doubled?

Answer:

Given,   side of square = 5 cm \[\therefore \]      Area of square \[=side\times side\]            \[=5\times 5\]            \[=25\text{ }sq\text{ }cm\]                                                                                                            Now according to question, New side \[=2\times \]initial side   \[=2\times 5\]    \[=10\text{ }cm\]                                                                                                                      \[\therefore \] Area of new square \[=side\times side\]           \[=10\times 10\]            \[=100\text{ }sq\text{ }cm\].                                                                                                       \[\therefore \] \[\frac{\text{Area}\,\,\text{of}\,\,\text{new}\,\,\text{square}}{\text{Area}\,\,\text{of}\,\,\text{old}\,\,\text{square}}=\frac{100}{25}=4\] Hence, the area of new square is 4 times increase.