Can the sides of a triangle have lengths 4, 6, and 8? Choices: (A)yes (B)no

Triangle Inequality Theorem: To determine if these side lengths can form 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 4 + 6 > 8: Check if 4 + 6 > 8. Calculation: 4 + 6 = 10, and 10 > 8, so this part is true. Check 4 + 8 > 6: Check if 4 + 8 > 6. Calculation: 4 + 8 = 12, and 12 > 6, so this part is true too. Check 6 + 8 > 4: Check if 6 + 8 > 4. Calculation: 6 + 8 = 14, and 14 > 4, so this part is also true. Final Verification: Since all parts of the triangle inequality are satisfied, the sides can indeed form a triangle.

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 $4$ , $6$ , and $8$ ? $\newline$ Choices: $\newline$ (A) yes $\newline$ (B) no

View step-by-step help

Full solution

Q. Can the sides of a triangle have lengths

4

6

, and

8

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Triangle Inequality Theorem: To determine if these side lengths can form 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 4 + 6 > 8: Check if 4 + 6 > 8. Calculation: $4 + 6 = 10$ , and 10 > 8, so this part is true.
Check 4 + 8 > 6: Check if 4 + 8 > 6. Calculation: $4 + 8 = 12$ , and 12 > 6, so this part is true too.
Check 6 + 8 > 4: Check if 6 + 8 > 4. Calculation: $6 + 8 = 14$ , and 14 > 4, so this part is also true.
Final Verification: Since all parts of the triangle inequality are satisfied, the sides can indeed form a triangle.