Maths-
General
Easy
Question
Describe the possible lengths of the third side of the triangle given the lengths of the other two sides.
5 inches, 12 inches
The correct answer is: Hence, all numbers between 7 and 17 will be the length of third side.
Answer:
- Hints:
- 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
- Step-by-step explanation:
- Given:
In triangle, sides are 5 inches and 12 inches.
a = 5 inches, b = 12 inches.
- Step-by-step explanation:
- Given:
In triangle, sides are 5 inches and 12 inches.
a = 5 inches, b = 12 inches.
- Step 1:
- Find length of third side.
According to triangle inequality theorem,
c < a + b
∴ c < 5 + 12
c < 17
- Step 1:
- Find length of third side.
According to triangle inequality theorem,
c < a + b
∴ c < 5 + 12
c < 17
- Step 2:
difference of two side < third side < sum of two sides
- Step 2:
b – a < c < a + b
12 – 5 < c < 5 + 12
7 < c < 17
Hence, all numbers between 7 and 17 will be the length of third side.
- Final Answer:
Hence, all numbers between 7 and 17 will be the length of third side.
- Triangle inequality theorem
- According to this theorem, in any triangle, sum of two sides is greater than third side,
- a < b + c
- while finding possible lengths of third side use below formula
- Given:
- Given:
- Step 1:
- Find length of third side.
- Step 1:
- Find length of third side.
- Step 2:
- Step 2:
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