Question

Which set of three numbers could be the side lengths of a triangle?

Answer 1

Answer:

The correct option is C.

Step-by-step explanation:

In a triangle, then sum of two smaller sides is greater than the length of third greatest side.

Let, in a triangle ABC, If the length of sides are $a$, then

$c$

In option A,

$8\nless 2+4$

Therefore option A is incorrect.

In option B,

$6\nless 2+4$

Therefore option B is incorrect.

In option C,

$7$

Therefore option C is correct.

In option D,

$9\nless 3+5$

Therefore option D is incorrect.

Answer 2

Answer:

C. 3, 5, 7

Step-by-step explanation:

We know that in a triangle, 'the sum of lengths of two sides is always greater than the length of the third side'.

So, according to our options:

A. In 2, 4, 8. We have 2 + 4 = 6 < 8

B. In 2, 4, 6. We see that, 2 + 4 = 6

C. In 3, 5, 7. We see that, 3 + 5 = 8 > 7

D. In 3, 5, 9. We see that, 3 + 5 = 8 < 9.

Therefore, only option C satisfies the property of the triangle stated above.

Hence, 3, 5, 7 are the side lengths of a triangle.