Question

Suppose triangle TIP and triangle TOP are isosceles triangles. Also suppose that TI=5, PI=7, and PO=11. What is the sum of all possible lengths for TP?

Answer 1

5,7

Explanation:

Two sides of TIP have lengths 5 and 7. Since triangle TIP is isosceles, the third side must be either 5 or 7. Both are possible, so the possible lengths for TP are 5,7. (We can have TO= PO=11 in either case to make triangle TOP an isosceles triangle. If TP=7, it is also possible to have TO=TP=7 to make triangle TOP isosceles)

Answer 2

The sum of all possible lengths for TP is 12

Explanation:

Given that triangle TIP and triangle TOP are isosceles triangles with sides;

TI = 5, PI = 7, PO = 11

Therefore, given that triangle TIP is an isosceles triangle, the length of segment TP will be equal either the length of segment TI or segment PI which give;

TP = TI 5 or TP = PI = 7

The sum of all possible lengths for TP is given by the sum of the two unequal sides of triangle TIP which gives;

The sum of all possible lengths for TP = 5 + 7 = 12.