Question

A wire is bent in the form of rectangle having length twice its breadth .the same wire is bent in the form of circle .it is found that the area of circle is greater than that of rectangle by 104.5 cm2 . Find length of wire.
Please answer in detail

Answer 1

Answer:

1. 66 cm

Step-by-step explanation:

Given, l = 2b

Perimeter of rectangle = 2 (l+b) = 2(2b+b) = 2(3b) = 6b

Area of rectangle = lb = (2b) * b = 2$b^{2}$

Later it is bent in form of circle,

Perimeter of circle = 2 * π * r = 6b

π * r = 3b

$\frac{22}{7}$ * r = 3b

r = $\frac{3*7 b}{22}$

r = $\frac{21 b}{22}$

Area of circle -  Area of rectangle = 104.5$cm^{2}$

(π * r )* r - 2$b^{2}$ = 104.5

3b * r - 2$b^{2}$ = 104.5

b ( 3r - 2b) = 104.5

104.5 = b ( 3r - 2b)

         = b (3$\frac{21 b}{22}$ - 2b)

         = b ( $\frac{63 b}{22}$ - 2b)

         = b ( $\frac{63 b - 44b}{22}$ )

         = b ( $\frac{19b}{22}$ )

104.5 * 22 = 19 $b^{2}$

2299 / 19 =  $b^{2}$

121 = $b^{2}$                

$b^{2}$ = 121

b = $\sqrt{121}$ = 11cm

Length of wire = 6b = 6 (11) = 66cm