Question

IF THE PERMITER OF A CIRCLE IS A EQUAL TO THAT OF A SQUARE THEN FIND THE RATIO OF THEIR AREAS.


plz plz answer

Answer 1

$\textbf{ \underline{ \large{ Hello Mate! }}}$

Perimter of circle = 2 × pie × r (circumference)

Perimter of square = 4s

As both perimeters are equal so

4s = 2 × pie × r
s = ( 2 × pie × r ) / 4

Area of circle = pie × r^2

Area of square = s^2

Ratio of their areas will be =

$\frac{\pi {r}^{2} }{ {s}^{2} } = \frac{\pi {r}^{2} }{ {( \frac{2\pi \: r}{4}) }^{2} } \\ = \frac{\pi {r}^{2} }{4 {\pi}^{2} {r}^{2} } \times 16 \\ = \frac{16}{4\pi} = \frac{16}{4 \times \frac{22}{7} } = \frac{16 \times 7}{4 \times 22} \\ = \frac{112}{88} = \frac{28}{22} = \frac{14}{11}$

$\boxed{ Hence\:ratio\:of\:areas\:are\: 14:11 }$

Have great future ahead!