Question

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

A. 2, 4, 8
B. 2, 4. 6
C. 3, 5, 7
D. 3, 5, 9

Answer 1

C. 3, 5, 7

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.

Answer 2

The correct option is C.

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<b<c`, then

`c<a+b`

In option A,

`8\\less 2+4`

Therefore option A is incorrect.

In option B,

`6\\less 2+4`

Therefore option B is incorrect.

In option C,

`7<3+5`

Therefore option C is correct.

In option D,

`9\\less 3+5`

Therefore option D is incorrect.