Question 123630
Let x=length of equal leg, y= length of base



Since the perimeter is equal to the sum of all three sides, the perimeter is


{{{P=x+x+y}}}


which simplifies to 


{{{P=2x+y}}}


Since the " lengths of the two equal legs are 6 in. less than 3 times the length of the base", this means {{{x=3y-6}}}


 {{{P=2x+y}}}  Start with the given formula


{{{37=2(3y-6)+y}}} Plug in {{{P=37}}}  and  {{{x=3y-6}}}


{{{37=6y-12+y}}} Distribute




{{{37=7y-12}}} Combine like terms on the right side



{{{0=7y-12-37}}}Subtract 37 from both sides



{{{-7y=-12-37}}} Subtract 7y from both sides



{{{-7y=-49}}} Combine like terms on the right side



{{{y=(-49)/(-7)}}} Divide both sides by -7 to isolate y




{{{y=7}}} Divide



Since we know that {{{y=7}}}, we can plug this into {{{x=3y-6}}} to find x



{{{x=3y-6}}} Start with the given equation


{{{x=3(7)-6}}} Plug in {{{y=7}}}


{{{x=21-6}}} Multiply


{{{x=15}}} Subtract



So the length of the equal leg is 15 and the length of the base is 7