Question

You're looking for a relationship between the squares of the side lengths of the right triangle.
Keep going. b is 2. What is b
2
? In other words, what is the area of a square with side length 2? You can think of this as: what is 2
2
?
a = 5b = 2 c =
29
​
a
2
= 25c
2
= ?b
2
= ?
a
2
b
2
c
2

25
?

Answer 1

To find the relationships between the squares of the side lengths of a right triangle where \( a \), \( b \), and \( c \) represent the lengths of the sides, we use the Pythagorean theorem. In a right triangle, the relationship is given by:

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

From your information:
- \( b = 2 \)
- We need to calculate \( b^2 \):

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

You also stated \( a = 5 \). Therefore, we calculate \( a^2 \):

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

Now, you mentioned \( c \) with a placeholder for its value; we will calculate \( c^2 \):

Using the Pythagorean theorem \( a^2 + b^2 = c^2 \):
\[
c^2 = a^2 + b^2 = 25 + 4 = 29
\]

So, the values you are looking for are:
- \( a^2 = 25 \)
- \( b^2 = 4 \)
- \( c^2 = 29 \)

Therefore, the complete information is:

\[
\begin{align*}
a^2 &= 25 \\
b^2 &= 4 \\
c^2 &= 29
\end{align*}
\]