Question 830276
The two gardens are similar figures, so the ratio of areas is the square of the ratio of any linear measurement, such as the circumference or the radius.
If the ratio of areas is {{{25=5^2}}}, the ratio of the circumferences is {{{5}}}, and the circumference of garden B is 5 times the circumference of garden A, or
{{{5*(1.760Km)=highlight(8.800Km)}}}
 
ANOTHER WAY:
{{{r}}}= radius of the small circle (garden A)
{{{a=pi*r^2}}}= area of the small circle (garden A)
{{{R}}}= radius of the large circle (garden B)
{{{A=pi*R^2}}}= area of the large circle (garden B)
The problem says that {{{A/a=25}}}
So, {{{pi*R^2/(pi*r^2)=25}}}
{{{R^2/r^2=25}}}
{{{(R/r)^2=25}}}
{{{(R/r)^2=5^2}}}
{{{R/r=5}}} --> {{{R=5r}}}
The circumference of the small circle (garden A) is {{{2pi*r=1.760Km}}} .
At this point we could solve for {{{r}}} , and then calculate {{{R}}} and then the circumference of garden B.
An easier way forward, is found think in a way a bit more abstract:
The circumference of the large circle (garden B) is
{{{2pi*R=2pi*(5r)=5(2pi*r)=5*(1.760Km)=highlight(8.800Km)}}}