Question

1. three side lengths of a triangle are shown. 9, 12, and 15 complete the statement about the triangle formed. a triangle formed with side lengths 9, 12, and 15 (is/ is not) a right triangle. its hypotenuse is ____. or it does not have a hypotenuse.

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse (longest side), \(a\) and \(b\) are the other two sides.

Step2: Identify sides

Here, sides are 9, 12, 15. Longest side \(c = 15\), \(a = 9\), \(b = 12\).

Step3: Calculate \(a^2 + b^2\) and \(c^2\)

\(a^2 + b^2 = 9^2 + 12^2 = 81 + 144 = 225\)
\(c^2 = 15^2 = 225\)

Step4: Compare

Since \(9^2 + 12^2 = 15^2\), the triangle satisfies the Pythagorean theorem.

Answer:

A triangle formed with side lengths 9, 12, and 15 is a right triangle. Its hypotenuse is 15.