Two sides of a triangle measure 7 cm and 15 cm. Which could be the measure of the third side of the triangle?
7 cm
22 cm
18 cm
25 cm
Two sides of a triangle measure 7 cm and 15 cm. Which could be the measure of the third side of the triangle?
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To find the possible measure of the third side of a triangle when two sides are given, we can use the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let the two sides be (a = 7) cm and (b = 15) cm. We’ll analyze each option for the third side (c):
1. For (c = 7) cm:
– (7 + 7 > 15) (False)
– Not valid.
2. For (c = 22) cm:
– (7 + 15 > 22) (False)
– Not valid.
3. For (c = 18) cm:
– (7 + 15 > 18) (True)
– (7 + 18 > 15) (True)
– (15 + 18 > 7) (True)
– Valid option.
4. For (c = 25) cm:
– (7 + 15 > 25) (False)
– Not valid.
The only possible measure for the third side of the triangle is 18 cm.