A traffic sign has side lengths of 12.6 inches, 12.6 inches, and 12.6 inches. We want to determine whether the sign is a right triangle. Let's draw a sign and mark the given side lengths on it.
If the equation a^2 + b^2 = c^2 is true for the side lengths of a triangle, then the triangle is a right triangle.
We will substitute the side lengths for a, b, and c. Then, we will simplify to see if the equation produces a true statement. For simpler calculations, we will remove the units from the equation.
We obtained a false statement. Therefore, the sign is not a right triangle.
Alternative Solution
Congruent Sides of a Triangle
The side lengths of the given triangle are 12.6 inches each. This means that the sides of the triangle are all congruent. Let's think about one fact about the side lengths in a right triangle.
In a right triangle, the legs are the shorter sides and the hypotenuse is always the longest side.
When all of the sides have equal lengths, there is not a longest side. Since there is no longest side, the given triangle cannot be a right triangle.
