Question

a right triangle has a base of 12 units and a hypotenuse of 18 units. what is the length of the other leg? choose the correct answer. 6 units sqrt{180} units sqrt{468} units 30 units

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\), where \(c\) is hypotenuse, \(a,b\) are legs. Let base \(a = 12\), hypotenuse \(c = 18\), find \(b\).

Step2: Rearrange formula for \(b\)

\(b^2 = c^2 - a^2\)

Step3: Substitute values

\(b^2 = 18^2 - 12^2 = 324 - 144 = 180\)? Wait, no: \(18^2=324\), \(12^2 = 144\), \(324 - 144 = 180\)? Wait, no, wait: Wait, 324 - 144 is 180? Wait, no, 324 - 144: 324 - 100 = 224, 224 - 44 = 180? Wait, no, 1818=324, 1212=144, 324-144=180? Wait, but wait, the options: Wait, no, wait, maybe I miscalculated. Wait, 18 squared is 324, 12 squared is 144, 324 - 144 = 180? Wait, but the option is \(\sqrt{180}\)? Wait, no, wait, 18^2 - 12^2 = (18 - 12)(18 + 12) = 6*30 = 180. So \(b = \sqrt{180}\)? Wait, but wait, 18^2 is 324, 12^2 is 144, 324 - 144 is 180, so \(b = \sqrt{180}\). Wait, but let me check again. Wait, 18^2 is 324, 12^2 is 144, 324 - 144 = 180. So \(b = \sqrt{180}\). So the correct option is \(\sqrt{180}\) units. Wait, but wait, the options: the second option is \(\sqrt{180}\) units. So that's the answer.

Wait, no, wait, 18 squared is 324, 12 squared is 144, 324 - 144 is 180, so \(b = \sqrt{180}\). So the correct answer is \(\sqrt{180}\) units.

Answer:

\(\boldsymbol{\sqrt{180}}\) units (the option: \(\boldsymbol{\sqrt{180}}\) units)