The base of an isosceles triangle is half the length of each of its congruent sides. If the perimeter of the triangle is 120 inches, what is the length of the base?
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My goodness that is ugly. If the base is length x, then you know the other two sides are twice as long so they are 2x. Add all the sides up and set them equal to 120 and solve for x, and that will be the length of the base
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How do I know what the sides are?
Give me a minute I will type up a more thorough explanation for you
The problem states that we are dealing with an isosceles triangle. What information does that give us? An isosceles triangle is a triangle where two of the sides have the same length. The third side, the one which has a different length, is called the base.
This problem is telling us that the base is half the size of the sides. We do not know the actual lengths of the sides, but we know that if we added all of them up we would get 120. So we write down the equation:
(Length of side 1) + (Length of side 2) + (Length of side 3) = 120 inches.
We have to use algebra to solve this, so let's call the length of side 1 x, and say that is our base. If we know that the other sides are twice as long as the base, then we know that their length is equal to 2x. So our three sides have lenghts x, 2x, and 2x. We put those into the equation above:
x + 2x + 2x = 120
5x = 120
x = 24
And that should be the length of the base.