Question

A triangle has side with lengths of 65 feet, 69 feet, and 97 feet is it a right triangle?

Answer 1

To determine if a triangle with side lengths of 65 feet, 69 feet, and 97 feet is a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

First, we identify the longest side, which is 97 feet. The other two sides are 65 feet and 69 feet.

Now we check if the following holds true:

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

where \(c\) is the length of the longest side (97 feet), \(a\) is 65 feet, and \(b\) is 69 feet. Let's calculate:

1. Calculate \(c^2\):
\[
97^2 = 9409
\]

2. Calculate \(a^2 + b^2\):
\[
65^2 = 4225
\]
\[
69^2 = 4761
\]
\[
a^2 + b^2 = 4225 + 4761 = 8986
\]

Now, we compare \(c^2\) and \(a^2 + b^2\):

\[
9409 \neq 8986
\]

Since \(c^2\) is not equal to \(a^2 + b^2\), the triangle with sides of lengths 65 feet, 69 feet, and 97 feet is **not a right triangle**.