SOLUTION: the perimeter of an isosceles triangle is 72cm and the base is 4 cm shorter than the sum of the shorter sides what was the length of the base?

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Question 702281: the perimeter of an isosceles triangle is 72cm and the base is 4 cm shorter than the sum of the shorter sides what was the length of the base?
Answer by neatmath(302) About Me  (Show Source):
You can put this solution on YOUR website!

An isosceles triangle has exactly two congruent sides.

Let a stand for the length of those two congruent sides.

Let b stand for the length of the base.

Then we have:

Eq 1: 72=2%2Aa%2Bb given, because the perimeter P=a%2Ba%2Bb

Eq 2: b%2B4=a%2Ba given

So, let's begin:

b%2B4=2a simplifying Eq 2

b=2a-4

Now substitute this value for b into Eq 1:

72=2a%2B2a-4

72=4a-4

76=4a

19=a

Now substitute this value for a into Eq 2:

b%2B4=19%2B19

b%2B4=38

b=34

So the length of the base of our triangle is 34 cm.

Check it, it works!

I hope this helps! Keep practicing! :)

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