Question

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

a=3, b=4; or a=4,b=3. the c HAS to be the hypotenuse (longest side)

Explanation:

a^2 + b^2 = c^2

the a and b are interchangeable with the two legs of a right triangle. But the c term must represent the hypotenuse (longest/side opposite right angle)

Answer 2

see below

Explanation:

The Pythagorean theorem is the sum of the squares of the sides of the legs is equal to the square of the hypotenuse

a^2 + b^2 = c^2

The legs are a and b and the hypotenuse is c

The longest side is the hypotenuse. It must be the largest number since it is equal to the sum of the squares of the other two numbers

3^2 + 4^2 = 5^2

9+16=25

25=25