Question

A triangle has sides with lengths of 28 meters, 36 meters, and 45 meters. Is it a right triangle?
Yes or no
Show your work

Answer 1

To determine if the triangle with sides of lengths 28 meters, 36 meters, and 45 meters is a right triangle, we can use the Pythagorean theorem. The 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.

1. Identify the lengths of the sides:
- \( a = 28 \) meters
- \( b = 36 \) meters
- \( c = 45 \) meters (the longest side)

2. Apply the Pythagorean theorem:
\[
c^2 = a^2 + b^2
\]

3. Calculate \( c^2 \) and \( a^2 + b^2 \):
\[
c^2 = 45^2 = 2025
\]
\[
a^2 = 28^2 = 784
\]
\[
b^2 = 36^2 = 1296
\]
\[
a^2 + b^2 = 784 + 1296 = 2080
\]

4. Compare \( c^2 \) with \( a^2 + b^2 \):
- We have \( c^2 = 2025 \) and \( a^2 + b^2 = 2080 \).

Since \( c^2 \) (2025) is not equal to \( a^2 + b^2 \) (2080), the triangle is not a right triangle.

**Final answer: No, it is not a right triangle.**