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Which of the following values cannot be a possible value of x in the
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20 Jan 2025, 00:08
20 Jan 2025, 00:08
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Which of the following values cannot be a possible value of x in the above triangle?
A. 8
B. 9
C. 10
D. 11
E. 15
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Re: Which of the following values cannot be a possible value of x in the
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01 Mar 2025, 04:47
01 Mar 2025, 04:47
Expert Reply
We know that the sum of any two sides in a triangle is greater than the third side, using this rule, we can check from the options that which cannot be the value of $x$.
(A) 8 , we get the sides of the triangle as $13,12 \& 8$ for which the above rule holds true, so is a possible value of $x$.
(B) 9 , we get the sides of the triangle as $14,11 \& 9$ for which the above rule holds true, so is a possible value of $x$.
(C) 10 , we get the sides of the triangle as $15,10 \& 10$ for which the above rule holds true, so is a possible value of $x$.
(D) 11 , we get the sides of the triangle as $16,9 \& 11$ for which the above rule holds true, so is a possible value of $x$.
(E) 15 , we get the sides of the triangle as $20,5 \& 15$, where $15+5=20$ is not greater than 20 , so is NOT a possible value of $x$.
Hence the answer is (E).
(A) 8 , we get the sides of the triangle as $13,12 \& 8$ for which the above rule holds true, so is a possible value of $x$.
(B) 9 , we get the sides of the triangle as $14,11 \& 9$ for which the above rule holds true, so is a possible value of $x$.
(C) 10 , we get the sides of the triangle as $15,10 \& 10$ for which the above rule holds true, so is a possible value of $x$.
(D) 11 , we get the sides of the triangle as $16,9 \& 11$ for which the above rule holds true, so is a possible value of $x$.
(E) 15 , we get the sides of the triangle as $20,5 \& 15$, where $15+5=20$ is not greater than 20 , so is NOT a possible value of $x$.
Hence the answer is (E).
Re: Which of the following values cannot be a possible value of x in the
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01 Mar 2025, 04:48
01 Mar 2025, 04:48
1
Expert Reply
Alternate Method
We know that the sum of any two sides in a triangle is greater than the third side, using this rule, we get $(20-x)+x>x+5$ which when simplified gives $x<15$
Since the value of $x$ is to be strictly less than 15 , so 15 itself CANNOT be the value of $x$.
Hence the answer is (E).
We know that the sum of any two sides in a triangle is greater than the third side, using this rule, we get $(20-x)+x>x+5$ which when simplified gives $x<15$
Since the value of $x$ is to be strictly less than 15 , so 15 itself CANNOT be the value of $x$.
Hence the answer is (E).
