Question

A triangle has sides with lengths of 12 yard, 13 yards, and 15 yards. Which numbers are representing the legs of a triangle?

Answer 1

None of these sides represent the legs.

Step-by-step explanation

The legs of a triangle are the sides that form the right angle in a right triangle. The legs are always the shortest sides, while the hypotenuse is the longest side.

In this case, the hypotenuse would be 15 yards, while the legs would be 12 yards and 13 yards. For this to be a right triangle, the Pythagorean Theorem must be satisfied,

`\begin{gathered} 12^2+13^2=15^2 \\ 144+169=15^2 \\ 313=225\to false \end{gathered}`

These side lengths do not satisfy the Pythagorean Theorem and, therefore, this is not a right triangle. If it is not a right triangle, then it does not have legs. Hence, none of these represent the legs.