Question

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?

Answer 1

Answer: Which way(s) can you substitute the values into the equation to make it true? You could substitute the two side lengths 3 and 4 for a^2 and b^2 but you can’t substitute c^2. This is because the value isn’t high enough, if it was high enough it would have to match 5 is 25. 3 and 4 are the lengths of the shorter side and 5 is the length of the longest side (known as Hypotenuse). Which variable has to match the longest side length? Why? c^2 has to match the longest side of the triangle because the smaller numbers would end up causing the equation to be not true. (Just adding some of my own things I just learned….The hypotenuse is the square root of 25 as 5, which means that it is the longest side of the right angle/right triangle. It is also the side opposite to the 90-degree angle. )

For example: 3^2+4^2=5^2____4^2+3^2=5^2____9+16=25____16+9=25

AKA: Make sure to use your own word just in case okay? I don't want anyone to get in trouble out there yk? Ight..see ya!

Answer 2

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
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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!