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A triangle has sides of length 4.7 meters and 9 meters. Which of the following CANNOT be the length of the third side, in meters?
- a)5
- b)7
- c)8
- d)11
- e)14
Correct answer is option 'E'. Can you explain this answer?
Most Upvoted Answer
A triangle has sides of length 4.7 meters and 9 meters. Which of the f...
The key to solving this problem is remembering that the triangle inequality states that no one side of a triangle can be greater than the sum of the other two sides. Thus the third side of the triangle in the problem cannot be greater than the sum of the other two sides, 4.7 and 9, which is 13.7. Of the answer choices, only 14 is too large to be a possible value for the third side of the triangle.
Community Answer
A triangle has sides of length 4.7 meters and 9 meters. Which of the f...
Given:
- Length of one side of the triangle = 4.7 meters
- Length of another side of the triangle = 9 meters
To find:
Which of the following CANNOT be the length of the third side?
Solution:
Let's assume the length of the third side is 'x' meters.
In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Therefore, we can write the following inequalities:
1) 4.7 + 9 > x
2) 4.7 + x > 9
3) 9 + x > 4.7
Simplifying these inequalities, we get:
1) 13.7 > x
2) x > 4.3
3) x > -4.3
The length of a side cannot be negative, so we can ignore the third inequality. Combining the first two inequalities, we get:
4.3 < x="" />< />
Now, let's check each option to see if it falls within this range:
a) 5: 4.3 < 5="" />< 13.7="" -="" this="" is="" a="" valid="" length="" for="" the="" third="" />
b) 7: 4.3 < 7="" />< 13.7="" -="" this="" is="" a="" valid="" length="" for="" the="" third="" />
c) 8: 4.3 < 8="" />< 13.7="" -="" this="" is="" a="" valid="" length="" for="" the="" third="" />
d) 11: 4.3 < 11="" />< 13.7="" -="" this="" is="" a="" valid="" length="" for="" the="" third="" />
e) 14: 4.3 < 14="" />< 13.7="" -="" this="" is="" not="" a="" valid="" length="" for="" the="" third="" />
Therefore, the length of the third side CANNOT be 14 meters (option E).
- Length of one side of the triangle = 4.7 meters
- Length of another side of the triangle = 9 meters
To find:
Which of the following CANNOT be the length of the third side?
Solution:
Let's assume the length of the third side is 'x' meters.
In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Therefore, we can write the following inequalities:
1) 4.7 + 9 > x
2) 4.7 + x > 9
3) 9 + x > 4.7
Simplifying these inequalities, we get:
1) 13.7 > x
2) x > 4.3
3) x > -4.3
The length of a side cannot be negative, so we can ignore the third inequality. Combining the first two inequalities, we get:
4.3 < x="" />< />
Now, let's check each option to see if it falls within this range:
a) 5: 4.3 < 5="" />< 13.7="" -="" this="" is="" a="" valid="" length="" for="" the="" third="" />
b) 7: 4.3 < 7="" />< 13.7="" -="" this="" is="" a="" valid="" length="" for="" the="" third="" />
c) 8: 4.3 < 8="" />< 13.7="" -="" this="" is="" a="" valid="" length="" for="" the="" third="" />
d) 11: 4.3 < 11="" />< 13.7="" -="" this="" is="" a="" valid="" length="" for="" the="" third="" />
e) 14: 4.3 < 14="" />< 13.7="" -="" this="" is="" not="" a="" valid="" length="" for="" the="" third="" />
Therefore, the length of the third side CANNOT be 14 meters (option E).
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A triangle has sides of length 4.7 meters and 9 meters. Which of the following CANNOT be the length of the third side, in meters?a)5b)7c)8d)11e)14Correct answer is option 'E'. Can you explain this answer?
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