Question

a right triangle that has legs of lengths 9 inches and 12 inches has a hypotenuse with the length of (select) (select) 6 inches 11 inches 15 inches 21 inches

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a = 9\) and \(b=12\), and hypotenuse \(c\), the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\). So \(c^{2}=9^{2}+12^{2}\).

Step2: Calculate \(a^{2}\) and \(b^{2}\)

\(9^{2}=81\) and \(12^{2} = 144\). Then \(c^{2}=81 + 144\).

Step3: Sum the values

\(81+144=225\). So \(c^{2}=225\).

Step4: Find \(c\)

Take the square root of \(225\), \(c=\sqrt{225}\). Since \(\sqrt{225}=15\).

Answer:

15 inches