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Maths-

General

Easy

Question

A triangle has one side of length 12 and another of length 8. Describe the possible lengths of the third side.

hint Hint:

Triangle inequality theorem

According to this theorem, in any triangle, sum of two sides is greater than third side,

a < b + c

b < a + c

c < a + b

while finding possible lengths of third side use below formula

difference of two side < third side < sum of two sides

The correct answer is: Hence, all numbers between 4 and 20 will be the length of third side.

Step-by-step explanation:
Given:
In triangle, sides are 12 cm and 8 cm.
a = 12 cm, b = 8 cm.
Step 1:
Find length of third side.
According to triangle inequality theorem,
c < a + b
∴ c < 12 + 8
c < 20
Step 2:
difference of two side < third side < sum of two sides
a – b < c < a + b
12 – 8 < c < 12 + 8
4 < c < 20
Hence, all numbers between 4 and 20 will be the length of third side.
Final Answer:
Hence, all numbers between 4 and 20 will be the length of third side.

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