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In a triangle, the lengths of the two larger sides are 10 and 9, respectively. If the angles are in A P. Then the length of the third side can be
- a)5 -√6
- b)3√3
- c)5
- d)5 + √6
- e)none
Correct answer is option 'A,D'. Can you explain this answer?
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Verified Answer
In a triangle, the lengths of the two larger sides are 10 and 9, respe...
Since the angles of triangle are in A.P., Let ∠A = x – d, ∠B = x, ∠C = x + d
Then by ∠ sum property of triangle, we have ∠A +∠ B + ∠C = 180°
⇒ x – d + x + x + d = 180°
⇒ 3x = 180° ⇒ x = 60°
∴ ∠B = 60°
Then by ∠ sum property of triangle, we have ∠A +∠ B + ∠C = 180°
⇒ x – d + x + x + d = 180°
⇒ 3x = 180° ⇒ x = 60°
∴ ∠B = 60°
Given that a = 10, b = 9 are the longer sides
(both the values are less than 9 and 10),
both are possible.Most Upvoted Answer
In a triangle, the lengths of the two larger sides are 10 and 9, respe...
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Community Answer
In a triangle, the lengths of the two larger sides are 10 and 9, respe...
Let's use the triangle inequality theorem to find the possible range of lengths for the third side.
According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
So, we have:
10 + 9 > third side length
19 > third side length
Therefore, the third side must be less than 19.
Now, let's find the minimum possible length for the third side. The minimum occurs when the two larger sides are just barely touching each other, creating a degenerate triangle.
In this case, the third side length would be equal to the difference between the two larger sides:
10 - 9 = 1
Therefore, the minimum length for the third side is 1.
So, the length of the third side can be any value between 1 and 19.
Answer: a) 1 - 19
According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
So, we have:
10 + 9 > third side length
19 > third side length
Therefore, the third side must be less than 19.
Now, let's find the minimum possible length for the third side. The minimum occurs when the two larger sides are just barely touching each other, creating a degenerate triangle.
In this case, the third side length would be equal to the difference between the two larger sides:
10 - 9 = 1
Therefore, the minimum length for the third side is 1.
So, the length of the third side can be any value between 1 and 19.
Answer: a) 1 - 19
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In a triangle, the lengths of the two larger sides are 10 and 9, respectively. If the angles are in A P. Then the length of the third side can bea)5 -√6b)3√3c)5d)5 + √6e)noneCorrect answer is option 'A,D'. Can you explain this answer?
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