Question

which of the following are the possible side lengths for a triangle?

A. 2,4,6
B. 1,2,3
C. 5,9,15
D. 6,7,8​

Answer 1

Answer:

6,7,8

Step-by-step explanation:

right side possible for triangle for measuring the length...

Answer 2

Given : The given options for the side lengths of a triangle are -

• 2,4,6
• 1,2,3
• 5,9,15
• 6,7,8

To find : The option which is correct possibility for becoming the side lengths for a triangle.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to determine the correct option)

Now, we know that :

• The sum of any two sides of a triangle is always greater than its third side.

So, we will be checking the given options w.r.t the above mentioned mathematical property of the triangle.

Checking the first option (2,4,6)

• 1st + 2nd = 2+4 = 6
• 3rd = 6
• So, (1st + 2nd) = 3rd
• This option is incorrect (as the 1st + 2nd should be greater than the 3rd)
• No need to check other combinations of sum.

Checking the second option (1,2,3)

• 1st + 2nd = 1+2 = 3
• 3rd = 3
• So, (1st + 2nd) = 3rd
• This option is incorrect (as the 1st + 2nd should be greater than the 3rd)
• No need to check other combinations of sum.

Checking the third option (5,9,15)

• 1st + 2nd = 5+9 = 14
• 3rd = 15
• So, (1st + 2nd) < 3rd
• This option is incorrect (as the 1st + 2nd should be greater than the 3rd)
• No need to check other combinations of sum.

Checking the fourth option (6,7,8)

• 1st + 2nd = 6+7 = 13
• 3rd = 8
• So, (1st + 2nd) > 3rd

• 1st + 3rd = 6+8 = 14
• 2nd = 7
• So, (1st + 3rd) > 2nd

• 2nd + 3rd = 7+8 = 15
• 1st = 6
• So, (2nd + 3rd) > 1st

• Which means, sum of any two sides is greater than the remaining third side.
• This option is correct.

Hence, (6,7,8) are possible side lengths of a triangle.