Question

You're looking for a relationship between the squares of the side lengths of the right triangle.
a is 5. What is a
2
? In other words, what is the area of a square with side length 5? You can think of this as: what is 5
2
?
a = 5b = 2 c =
29
​
a
2
= ?c
2
= ?b
2
= ?
a
2
b
2
c
2

? ?

Answer 1

In a right triangle, the relationship between the squares of the lengths of the sides (a, b, and c, where c is the length of the hypotenuse) is given by the Pythagorean theorem, which states:

\[
c^2 = a^2 + b^2
\]

Given that \(a = 5\), we can find \(a^2\):

\[
a^2 = 5^2 = 25
\]

You mentioned that \(b = 2\). Let's find \(b^2\):

\[
b^2 = 2^2 = 4
\]

To find \(c^2\) using the Pythagorean theorem, we can substitute the values of \(a^2\) and \(b^2\):

\[
c^2 = a^2 + b^2 = 25 + 4 = 29
\]

So we have:

- \(a^2 = 25\)
- \(b^2 = 4\)
- \(c^2 = 29\)

Thus, the results are:

\[
a^2 = 25, \quad b^2 = 4, \quad c^2 = 29
\]