Question

You're looking for a relationship between the squares of the side lengths of the right triangle.
Does a
2
+b
2
=c
2
hold true for this right triangle? In other words, is the equation 25+4=29 true?
a = 5
b = 2
c=
29
​

a
2
+b
2

=
?

c
2

25 + 4
=
?

29
29
=
?

29
a
2
b
2
c
2

25 4 29

No, a
2
+b
2
=c
2
is not true for this right triangle.

Yes, a
2
+b
2
=c
2
is true for this right triangle.

Answer 1

To determine if \( a^2 + b^2 = c^2 \) holds true for the given side lengths of a right triangle with \( a = 5 \), \( b = 2 \), and \( c = 29 \), we can calculate each side.

1. Calculate \( a^2 \) and \( b^2 \):
- \( a^2 = 5^2 = 25 \)
- \( b^2 = 2^2 = 4 \)

2. Add \( a^2 \) and \( b^2 \):
\[
a^2 + b^2 = 25 + 4 = 29
\]

3. Calculate \( c^2 \):
- \( c^2 = 29^2 = 841 \)

Now we compare \( a^2 + b^2 \) to \( c^2 \):
- We found that \( a^2 + b^2 = 29 \) and \( c^2 = 841 \).

Since \( 29 \neq 841 \), we conclude that:

**No, \( a^2 + b^2 = c^2 \) is not true for this right triangle.**