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Can the sides of a triangle have lengths 2,4 and 6?

User Tan Sang
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2 Answers

6 votes

Answer:

NO

Explanation:

the sum of two sides of a triangle is larger than the third side

2 + 4 = 6

so

NO

User MagicLAMP
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8.2k points
5 votes

Answer:

NO

Explanation:

No, the sides of a triangle must satisfy the triangle inequality, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words, if a, b, and c are the lengths of the sides of a triangle, then:

a + b > c

b + c > a

a + c > b

Let's check whether the lengths 2, 4, and 6 satisfy this inequality:

2 + 4 > 6 ? Yes

4 + 6 > 2 ? Yes

2 + 6 > 4 ? Yes

All three inequalities are satisfied, so the lengths 2, 4, and 6 can form the sides of a triangle. However, we can also see that 6 is equal to the sum of 2 and 4, which means that these three lengths would form a degenerate triangle. A degenerate triangle is a triangle in which one or more sides have zero length, or the sides are collinear, which means they lie on the same straight line. In this case, the sides are collinear, so they cannot form a non-degenerate triangle. Therefore, the answer is no, the sides of a triangle cannot have lengths 2, 4, and 6.

User Aqif Hamid
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8.2k points

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