If two sides of a triangle are 9 cm and 15 cm in length, which COULD be the measure of the third side?
A 23 cm
B 24 cm
C 25 cm
D 26 cm
Possible Measure of the Third Side of a Triangle
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If two sides of a triangle are 9 cm and 15 cm in length, which COULD be the measure of the third side?
A 23 cm
B 24 cm
C 25 cm
D 26 cm
To determine the possible lengths of the third side of a triangle, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side.
Given sides (a = 9 , text{cm}) and (b = 15 , text{cm}), let’s denote the unknown side as (c).
The inequalities we need to satisfy are:
1. (a + b > c)
2. (a + c > b)
3. (b + c > a)
Substituting the values, we get:
1. (9 + 15 > c implies 24 > c)
2. (9 + c > 15 implies c > 6)
3. (15 + c > 9) (this is always true since (c) is positive)
From the first inequality, (c) must be less than 24. From the second inequality, (c) must be greater than 6. Thus, (c) can range between 6 cm and 24 cm.
Now, let’s evaluate the choices:
– A: 23 cm (valid, since (6 < 23 < 24))
– B: 24 cm (invalid, since (c) must be less than 24)
– C: 25 cm (invalid, since (25 >