Question 73296
Let x be the longest side and y be the shorter sides. If you have the two smaller sides equal to two thirds of the longest side it looks like this
{{{y=(2/3)x}}}
Since the perimeter is the sum of all the sides then
{{{P=x+y+y}}}
{{{161=x+(2/3)x+(2/3)x}}}Plug in 2/3x into y
{{{161=x+(4/3)x}}}Add like terms by finding common denominator
{{{161=(3x+4x)/3}}}Solve for x
{{{483=(7x)}}}Multiply both sides by 3
{{{69=x}}}Divide both sides by 7
So the longest side is 69 miles. Take two thirds of it to find the shorter side.
{{{y=(2/3)(69)}}}
{{{y=46}}}
So the shorter sides are 46 miles
Check:
Use the formula to find the perimeter
{{{P=x+y+y}}}
{{{161=69+46+46}}}
{{{161=161}}}Answer works