Question

Do the following side lengths satisfy the Pythagorean Theorem?  Lengths =14, 50, 48.

Answer 1

To determine if the lengths 14, 50, and 48 satisfy the Pythagorean Theorem, we need to check if the relationship \(a^2 + b^2 = c^2\) holds, where \(c\) is the longest side (hypotenuse) and \(a\) and \(b\) are the other two sides.

Here, the longest side is 50, so we will assign:
- \(a = 14\)
- \(b = 48\)
- \(c = 50\)

Now we will calculate \(a^2 + b^2\) and \(c^2\):

1. Calculate \(a^2\) and \(b^2\):
\[
a^2 = 14^2 = 196
\]
\[
b^2 = 48^2 = 2304
\]

2. Now add these two results:
\[
a^2 + b^2 = 196 + 2304 = 2500
\]

3. Now calculate \(c^2\):
\[
c^2 = 50^2 = 2500
\]

4. Now compare \(a^2 + b^2\) to \(c^2\):
\[
2500 = 2500
\]

Since \(a^2 + b^2 = c^2\) holds true, the lengths 14, 50, and 48 do satisfy the Pythagorean Theorem.