Question

The side of the square is 5 cm. How many times does the area increases, if the side of the square is doubled?
[3 marks]

Answer 1

Given, that the side of the square = 5 cm

Area of a square = Side$\times$Side
$\therefore$ Area of the square = 5 $\times$5 = 25 $c{m}^2$
[1 mark]

Now, according to the question,

New side = 2 $\times$ 5 = 10 cm
$\therefore$ Area of new square = Side$\times$Side = (10 $\times 10)c{m}^2$ = 100 $c{m}^2$
[1 mark]

$\frac{\text{Area of new square}}{\text{Area of old square}}=\frac{100}{25}$ = 4

Hence, the area of the new square increases by four times.
[1 mark]