SOLUTION: The lengths of two sides of a triangle of 8ft and 12ft. What are the possible lengths for a third side? A) 3ft B) 5ft C) 21ft D) 15ft E) 18ft F) 9ft

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Question 1153567: The lengths of two sides of a triangle of 8ft and 12ft. What are the possible lengths for a third side?
A) 3ft
B) 5ft
C) 21ft
D) 15ft
E) 18ft
F) 9ft
Found 3 solutions by MathLover1, ikleyn, MathTherapy:
Answer by MathLover1(20849)   (Show Source):
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The lengths of two sides of a triangle of and .
What are the possible lengths for a third side?
the sum of any sides of a triangle must be greater than the measure of the third side

Denoting the third side as :

.....eq.1

Also,

.....eq.1
and

.....eq.1 disregard negative number
from eq.1 and eq.2, we have
A) 3ft-> the possible length for a third side
B) 5ft->the possible length for a third side
C) 21ft-> the possible lengths for a third side
D) 15ft->the possible lengths for a third side
E) 18ft->the possible lengths for a third side
F) 9ft-> the possible lengths for a third side

Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website!
.

It is between the sum 8+12 = 20 ft and the difference 12-8 = 4 ft of the lengths of the two given sides,
excluding the extreme values of 4 ft and 20 ft.

When I say "the difference", I mean the POSITIVE difference, of course.

Options A) and C) do not work - they are not possible.

Other optional lengths from the list are possible.

Actually, there are INFINITELY MANY possible values for the length of the third side.

Answer by MathTherapy(10552)   (Show Source):
You can put this solution on YOUR website!

The lengths of two sides of a triangle of 8ft and 12ft. What are the possible lengths for a third side?
A) 3ft
B) 5ft
C) 21ft
D) 15ft
E) 18ft
F) 9ft

All of the above except: A) 3ft
C) 21ft.