Question

Do sides with lengths of 7.50 inches, 5.25 inches, and 11.75 inches form a right-angled triangle according to the Pythagorean theorem?

Answer 1

To determine if the sides 7.50 inches, 5.25 inches, and 11.75 inches form a right-angled triangle, we can use the Pythagorean theorem. According to this theorem, for a triangle with sides \(a\), \(b\), and \(c\) (where \(c\) is the longest side), the following must be true:

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

First, we identify the longest side. Among the sides: 7.50, 5.25, and 11.75 inches, the longest side is 11.75 inches.

Now, let:
- \(a = 5.25\)
- \(b = 7.50\)
- \(c = 11.75\)

Next, we calculate \(a^2\), \(b^2\), and \(c^2\):

\[
a^2 = (5.25)^2 = 27.5625
\]
\[
b^2 = (7.50)^2 = 56.25
\]
\[
c^2 = (11.75)^2 = 138.0625
\]

Now, we will check if the sum of \(a^2\) and \(b^2\) equals \(c^2\):

\[
a^2 + b^2 = 27.5625 + 56.25 = 83.8125
\]

Now compare \(a^2 + b^2\) with \(c^2\):

\[
c^2 = 138.0625
\]

Since \(83.8125 \neq 138.0625\), we find that:

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

Therefore, the sides 7.50 inches, 5.25 inches, and 11.75 inches do not form a right-angled triangle according to the Pythagorean theorem.