Question 1206181: Select all of the following that can be used to construct a triangle if two sides of
the triangle have lengths of 7 centimeters and 10 centimeters (cccc).
3 cm
7 cm
10 cm
17 cm
18 cm
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52803)   (Show Source):
You can put this solution on YOUR website! .
Select all of the following that can be used to construct a triangle if two sides of
the triangle have lengths of 7 centimeters and 10 centimeters.
(a) 3 cm
(b) 7 cm
(c) 10 cm
(d) 17 cm
(e) 18 cm
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In order for three segments of the given length could form a triangle,
the triangle inequalities must be valid:
+-----------------------------------------------------+
| The sum of the lengths of any two sides |
| is greater than the length of the third side. |
+-----------------------------------------------------+
Having it, we see that
(a) triangle (7,10,3) is not possible, since 7+3 is equal to 10, but is not greater than 10.
(b) triangle (7,10,7) is possible, since all three triangle inequalities are satisfied.
(c) triangle (7,10,10) is possible, since all three triangle inequalities are satisfied.
(d) triangle (7,10,17) is not possible, since 7+10 is equal to 17, but is not greater than 17.
(e) Solve it on your own, based on given instructions.
The solution is fully explained.
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It may be interesting to you to learn that the triangle inequality is in one logical step
from the axiom, saying that the straight line is the shortest distance between two points in a plane.
! Only one logical step !
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
Refer to example 3 and example 4 of this lesson
a = 7
b = 10
b-a < c < b+a
10-7 < c < 10+7
3 < c < 17
If a triangle has sides 7 cm and 10 cm, then the missing side is somewhere between 3 cm and 17 cm where we exclude both endpoints.
Meaning that c = 3 isn't possible, and neither is c = 17.
Of the given answer choices, 7 cm and 10 cm fit the description above.
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