Question

1. if the legs of a right triangle are 5 units and 12 units, what is the length of the hypotenuse?

a. 15 units
b. 10 units
c. 14 units
d. 13 units

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Here \(a = 5\) and \(b = 12\).
So \(c^{2}=5^{2}+12^{2}\).

Step2: Calculate squares

\(5^{2}=25\) and \(12^{2}=144\). Then \(c^{2}=25 + 144=169\).

Step3: Find the square - root

\(c=\sqrt{169}=13\) (we take the positive square - root since length cannot be negative).

Answer:

d. 13 units