SOLUTION: A banner in the shape of an isosceles triangle has a base that is 2 inches shorter than either of the equal sides. If the perimeter of the banner is 43 inches, then what is the len

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Question 211581: A banner in the shape of an isosceles triangle has a base that is 2 inches shorter than either of the equal sides. If the perimeter of the banner is 43 inches, then what is the length of the equal sides?
Thx
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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%2By%2Bz. 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%2By%2Bz Start with the given equation.


43=z-2%2Bz%2Bz Plug in P=43 (the given perimeter), x=z-2, and y=z


43=3z-2 Combine like terms.


43%2B2=3z Add 2 to both sides.


45=3z Combine like terms.


%2845%29%2F3=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