Question 211581
Recall that the perimeter of any triangle is


P = length of side1 + length of side2 + length of side3



Now let

x = length of side1
y = length of side2
z = length of side3


So the perimeter is now {{{P=x+y+z}}}. Because the triangle is an isosceles, there are two sides that are equal. So let's make {{{y=z}}} which will make the base be 'x'. Since the "triangle has a base that is 2 inches shorter than either of the equal sides", this means {{{x=y-2}}} or {{{x=z-2}}}



{{{P=x+y+z}}} Start with the given equation.



{{{43=z-2+z+z}}} Plug in {{{P=43}}} (the given perimeter), {{{x=z-2}}}, and {{{y=z}}}



{{{43=3z-2}}} Combine like terms.



{{{43+2=3z}}}  Add {{{2}}} to both sides.



{{{45=3z}}} Combine like terms.



{{{(45)/3=z}}} Divide both sides by {{{3}}} to isolate {{{z}}}.



{{{15=z}}} Reduce.



{{{z=15}}} Rearrange the equation.



Since {{{y=z}}}, we know that {{{y=15}}} also. So the length of the equal sides is 15 inches. Subtract 2 from this to get 13



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Answer:



So the triangle has side lengths of 13, 15, and 15 inches