Answer:
The Pythagorean Theorem states that in a right-angled 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. This can be written as:
\[ c^2 = a^2 + b^2 \]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the other two sides.
To determine if the triangle UVW with sides of 7 inches, 9 inches, and 11 inches is a right triangle, we need to check if these sides satisfy the Pythagorean Theorem.
Let's assume the longest side, which is 11 inches, is the hypotenuse. We'll then check if:
\[ 11^2 = 7^2 + 9^2 \]
Let's calculate this.
The triangle with sides 7 inches, 9 inches, and 11 inches does not satisfy the Pythagorean Theorem, which means it is not a right triangle. The squares of the lengths of the sides do not add up to equal the square of the longest side.
Step-by-step explanation:
