MATH SOLVE

9 months ago

Q:
# PLEASE HELP!For any right triangle, the side lengths of the triangle can be put in the equation a2 + b2 = c2 where a, b, and c are the side lengths. A triangle with the side lengths 3 inches, 4 inches, and 5 inches is a right triangle. Which way(s) can you substitute the values into the equation to make it true? Which variable has to match the longest side length? Why?

Accepted Solution

A:

The short answer is trial and error. The side lengths "3" and "4" can both be substituted for a² and b² but not c² because their value squared is not high enough since 5² is 25. "c²" as to match the longest side because the smaller numbers will cause the equation to not be true. See Below.

a² + b² = c²

3² + 4² = 5²

9 + 16 = 25

25 = 25

______________________________

a² + b² = c²

4² + 3² = 5²

16 + 9 = 25

25 = 25

______________________________

a² + b² = c²

5² + 4² = 3²

25 + 16 = 9

41 ≠ 9

______________________________

a² + b² = c²

3² + 5² = 4²

9 + 25 = 16

34 ≠ 16

Hope this helped!

a² + b² = c²

3² + 4² = 5²

9 + 16 = 25

25 = 25

______________________________

a² + b² = c²

4² + 3² = 5²

16 + 9 = 25

25 = 25

______________________________

a² + b² = c²

5² + 4² = 3²

25 + 16 = 9

41 ≠ 9

______________________________

a² + b² = c²

3² + 5² = 4²

9 + 25 = 16

34 ≠ 16

Hope this helped!