Question

You're looking for a relationship between the squares of the side lengths of the right triangle.
Now, add 25 + 4 on the left side of the equation to see if it equals the right side of the equation.
a = 5
b = 2
c=
29
​

a
2
+b
2

=
?

c
2

25 + 4
=
?

29
=
?

29
a
2
b
2
c
2

25 4 29

Answer 1

To verify the relationship between the squares of the side lengths of the right triangle, we will use the Pythagorean theorem, which states that for a right triangle with legs \(a\) and \(b\) and hypotenuse \(c\):

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

Given the values:
- \(a = 5\)
- \(b = 2\)

Now, let's calculate the squares of \(a\) and \(b\):

\[
a^2 = 5^2 = 25
\]
\[
b^2 = 2^2 = 4
\]

Now, we sum \(a^2\) and \(b^2\):

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

Now let's find \(c^2\):

We know from your information that \(c\) is the hypotenuse. Thus,

\[
c^2 = 29
\]

Now, we can also determine \(c\):

\[
c = \sqrt{29}
\]

All together, we can summarize:

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

Thus, we have confirmed that:

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

So indeed, \(29 = 29\).
This holds true for the given values, verifying the Pythagorean theorem for this right triangle!