Explanation:
Not a right triangle.
To determine if a triangle is a right triangle, we can apply the Pythagorean theorem. According to the theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Let's calculate:
The given side lengths are:
Side A: 11 feet
Side B: 9 feet
Side C: 14 feet (hypotenuse)
According to the Pythagorean theorem, if the triangle is a right triangle, then:
Side A^2 + Side B^2 = Side C^2
Substituting the values:
11^2 + 9^2 = 14^2
121 + 81 = 196
202 ≠ 196
Since 202 is not equal to 196, we can conclude that the triangle with side lengths 11 feet, 9 feet, and 14 feet is not a right triangle.