Question
Is it possible to build a triangle using the given side lengths? If so, order the angles measures of the triangle from least to greatest.
𝑆𝑇 = √29, 𝑇𝑈 = 2√17, 𝑆𝑈 = 13.9
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
The correct answer is: No, it is not possible to construct triangle with this sides.
Answer:
- Step-by-step explanation:
Given:
In triangle,
ST = 5.38,
TU = 8.24
SU = 13.9,
Step 1:
First check validity.
According to triangle inequality theorem,
a < b + c,
5.38 < 8.24 + 13.9
5.38 < 22.14, True
b < a + c,
8.24 < 5.38 + 13.9,
8.24 < 19.28, True
c < a + b,
13.9 < 5.38 + 8.24
13.9 < 13.62, false
As sides of triangle does not satisfy triangle inequality theorem.
Hence, triangle cannot be constructed with this sides
Final Answer:
No, it is not possible to construct triangle with this sides.
Step 1:
First check validity.
According to triangle inequality theorem,
As sides of triangle does not satisfy triangle inequality theorem.
Hence, triangle cannot be constructed with this sides
Final Answer:
No, it is not possible to construct triangle with this sides.
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