Question

Suppose triangle TIP and triangle TOP are isosceles triangles. Also suppose that TI=5, PI=7, and PO=11. What are all the possible lengths TP? Enter the possible values, separated by commas.

Answer 1

5, 7.

Explanation:

If both triangles are isosceles, then, for each triangle, two of their sides must be equal. Since TI and PI are different, then TP is either equal to TI or PI.

That being said, TO will necessarily be equal to PO, which is 11, and the possible values for TP are:

If TP = TI, then TP = 5

If TP = PI. then TP = 7.