Question
Describe the possible values of x.
The correct answer is: Hence, all numbers between 1.6 and 15 are possible values of x.
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
- Step-by-step explanation:
- Given:
In triangle,
a = x + 11, b = 2x + 10, and c = 5x - 9.
- Step 1:
- First check validity.
According to triangle inequality theorem,
c - b < a < b + c,
(5x – 9) – (2x + 10) < x + 11 < (2x + 10) + (5x – 9)
3x - 19 < x + 11 < 7x + 1
First consider,
- Step 1:
- First check validity.
According to triangle inequality theorem,
c - b < a < b + c,
(5x – 9) – (2x + 10) < x + 11 < (2x + 10) + (5x – 9)
3x - 19 < x + 11 < 7x + 1
First consider,
- Step 1:
- First check validity.
According to triangle inequality theorem,
c - b < a < b + c,
(5x – 9) – (2x + 10) < x + 11 < (2x + 10) + (5x – 9)
3x - 19 < x + 11 < 7x + 1
First consider,
x + 11 < 7x + 1,
11 – 1 < 7x - x
10 < 6x
1.6 < x
Now, consider,
3x - 19 < x + 11
3x - x < 11 + 19
2x < 30
x < 15
therefore,
1.6 < x < 15
x < 15
- Final Answer:
Hence, all numbers between 1.6 and 15 are possible values of x.
- Triangle inequality theorem
- According to this theorem, in any triangle, sum of two sides is greater than third side,
- a < b + c
- Given:
- Step 1:
- First check validity.
- Step 1:
- First check validity.
- Step 1:
- First check validity.
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