Can the sides of a triangle have lengths 2, 6, and 7? Choices: (A)yes (B)no

Check Triangle Inequality: To determine if these can be the sides of a triangle, we need to check the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Check 2 + 6 > 7: Check if 2 + 6 > 7. Calculation: 2 + 6 = 8, and 8 > 7, so this part is true. Check 2 + 7 > 6: Check if 2 + 7 > 6. Calculation: 2 + 7 = 9, and 9 > 6, so this part is true too. Check 6 + 7 > 2: Check if 6 + 7 > 2. Calculation: 6 + 7 = 13, and 13 > 2, so this part is also true.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Can the sides of a triangle have lengths $2$ , $6$ , and $7$ ? $\newline$ Choices: $\newline$ (A) yes $\newline$ (B) no

View step-by-step help

Full solution

Q. Can the sides of a triangle have lengths

2

6

, and

7

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Check Triangle Inequality: To determine if these can be the sides of a triangle, we need to check the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Check 2 + 6 > 7: Check if 2 + 6 > 7. Calculation: $2 + 6 = 8$ , and 8 > 7, so this part is true.
Check 2 + 7 > 6: Check if 2 + 7 > 6. Calculation: $2 + 7 = 9$ , and 9 > 6, so this part is true too.
Check 6 + 7 > 2: Check if 6 + 7 > 2. Calculation: $6 + 7 = 13$ , and 13 > 2, so this part is also true.