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A triangle has two sides of lengths 7 and 12. What value could the length of
the third side be? Check all that apply.
A.7
B.5
C.9
D.3
E.17
F.11

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Answer:

A. 7

Step-by-step explanation:

Since the triangle sides are not defined, therefore let the base side have the 12 unit and one of the slant side be 7 unit.

Therefore height of the triangle, h can gotten from the Pythagoras theorem as thus:

7² = (12/2)² + h²

49 = 36 + h²

h² = 49 - 36 = 13

h = √13

knowing the height of the triangle, we can apply same rule to the other unknown slant side, x as thus:

x² = (12/2)² + h²

x² = 36 + 13 = 49

x = √49

x = 7

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