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# isoscles triangle sum of lengths

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Suppose  TOP and  TIP are isosceles triangles. Also suppose that TI = 5 and PI = 7 and PO=11.

What is the sum of all possible lengths for TO?

Guest Nov 2, 2017
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#1
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Since TIP is an isosceles triangle, either TP matches TI, therefore TP = 5

or TP matches PI, therefore TP = 7.

Since TOP is an isoscels triangle, either TO matches PO, therefore TO = 11

or TO matches TP when TP = 5, therefore TO = 5

or TO matches TP when TP = 7, therefore TP = 7.

The sum of all possible lengths for TO = 11 + 5 + 7 = 23.

geno3141  Nov 2, 2017
#2
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Thank you for trying... but that's not the right answer.  The hint says " don't forget the triangle inequality".  Can't the length possibly be 11 or 10 or 9... or 1?

Guest Nov 2, 2017
#3
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Okay, I got it!  11 + 7 = 18

Guest Nov 3, 2017

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