Question

Can u plz answer this ques. w/ an explanation?



The sides of the triangle have lengths 9, 13, k where k is an integer. For how many values of k is the triangle
obtuse?

Answer 1

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The sides of the triangle have lengths 9, 13, k where k is an integer. For how many values of k is the triangle obtuse?

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Sum of two sides of triangle is more than third side

⇒ 9+13>k

⇒ 22>k ⇒ k<22

Difference of any two sides of triangle is less than third side

⇒ 13 - 9 < k ⇒ 4<k ⇒ k>4

⇒ 4<k<22

⇒ k=5,6,7,....., 22

Triangle is obtuse,

⇒ either 9² + 13² < k² or 9² + k² < 13²

9² + 13² < k² ⇒ k = 17, 18, 19 ...., 22

9² + k² < 13² ⇒ 4, 5, 6 ....9

Number of values possible for k are

∴6 + 5 = 11 (Answer).

Step-by-step explanation:

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Answer 2

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The sides of the triangle have lengths 9, 13, k where k is an integer. For how many values of k is the triangle obtuse?

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Sum of two sides of triangle is more than third side

⇒ 9+13>k

⇒ 22>k ⇒ k<22

Difference of any two sides of triangle is less than third side

⇒ 13 - 9 < k ⇒ 4<k ⇒ k>4

⇒ 4<k<22

⇒ k=5,6,7,....., 22

Triangle is obtuse,

⇒ either 9² + 13² < k² or 9² + k² < 13²

9² + 13² < k² ⇒ k = 17, 18, 19 ...., 22

9² + k² < 13² ⇒ 4, 5, 6 ....9

Number of values possible for k are

Number of values possible for k are∴6 + 5 = 11 (Answer).

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