Question 73296
From the problem description, we can see that the triangle is an isosceles triangle. So we let the two equal sides be of length a and the third side, length b.
As you no doubt already know, the perimeter of a triangle is equal to the sum of the three sides, so P = a+a+b = 2a+b
But you are told that p = 161 miles, so now you can write the equation required to solve the problem:
161 = 2a+b
You also know that each of the two equal sides (a) is equal to two-thirds of the third side (b). This can be written: {{{a = (2/3)b}}}.  Now you want to substitute this relationship into the equation for the perimeter.
{{{161 = 2(2/3)b+b}}} Simplify and solve for b.
{{{161 = (4/3)b+b}}}
{{{161 = (7/3)b}}} Multiply both sides by the multiplicative inverse of {{{7/3}}}, that's {{{3/7}}}.
{{{161(3/7) = b}}} Simplify.
{{{23*3 = b}}}
{{{b = 69}}}mil;es. This is the length of the longest side.
{{{a = (2/3)b}}}
{{{a = (2/3)69}}}
{{{a = 46}}}miles. This is the length of each of the short sides.
Check:
46+46+69 = 161