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What is answer of this question. The length of two sides of a triangle are 4cm and 6cm.Between what two measures should the length of the third side fall ?
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What is answer of this question. The length of two sides of a triangle...
Triangle Inequality Theorem
To determine the possible lengths of the third side of a triangle when two sides are given, we apply 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.
Given Side Lengths
- Side A = 4 cm
- Side B = 6 cm
Applying the Theorem
According to the Triangle Inequality Theorem, the length of the third side (let's call it Side C) must satisfy the following conditions:
1. Side A + Side B > Side C
2. Side A + Side C > Side B
3. Side B + Side C > Side A
Calculating the Range for Side C
Let's evaluate these inequalities step-by-step:
- From the first condition:
4 cm + 6 cm > Side C
10 cm > Side C
Thus, Side C < 10="" />
- From the second condition:
4 cm + Side C > 6 cm
Side C > 6 cm - 4 cm
Side C > 2 cm.
- From the third condition:
6 cm + Side C > 4 cm
Side C > 4 cm - 6 cm
Since this condition is always satisfied when Side C is positive, we focus on the previous two inequalities.
Conclusion
Combining the results, we find that the length of Side C must fall within the following range:
- 2 cm < side="" c="" />< 10="" />
Thus, the possible length of the third side must be greater than 2 cm and less than 10 cm.
To determine the possible lengths of the third side of a triangle when two sides are given, we apply 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.
Given Side Lengths
- Side A = 4 cm
- Side B = 6 cm
Applying the Theorem
According to the Triangle Inequality Theorem, the length of the third side (let's call it Side C) must satisfy the following conditions:
1. Side A + Side B > Side C
2. Side A + Side C > Side B
3. Side B + Side C > Side A
Calculating the Range for Side C
Let's evaluate these inequalities step-by-step:
- From the first condition:
4 cm + 6 cm > Side C
10 cm > Side C
Thus, Side C < 10="" />
- From the second condition:
4 cm + Side C > 6 cm
Side C > 6 cm - 4 cm
Side C > 2 cm.
- From the third condition:
6 cm + Side C > 4 cm
Side C > 4 cm - 6 cm
Since this condition is always satisfied when Side C is positive, we focus on the previous two inequalities.
Conclusion
Combining the results, we find that the length of Side C must fall within the following range:
- 2 cm < side="" c="" />< 10="" />
Thus, the possible length of the third side must be greater than 2 cm and less than 10 cm.
Community Answer
What is answer of this question. The length of two sides of a triangle...
between 2 to 12
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What is answer of this question. The length of two sides of a triangle are 4cm and 6cm.Between what two measures should the length of the third side fall ?
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What is answer of this question. The length of two sides of a triangle are 4cm and 6cm.Between what two measures should the length of the third side fall ? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about What is answer of this question. The length of two sides of a triangle are 4cm and 6cm.Between what two measures should the length of the third side fall ? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is answer of this question. The length of two sides of a triangle are 4cm and 6cm.Between what two measures should the length of the third side fall ?.
What is answer of this question. The length of two sides of a triangle are 4cm and 6cm.Between what two measures should the length of the third side fall ? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about What is answer of this question. The length of two sides of a triangle are 4cm and 6cm.Between what two measures should the length of the third side fall ? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is answer of this question. The length of two sides of a triangle are 4cm and 6cm.Between what two measures should the length of the third side fall ?.
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