Question

find the length of the third side. if necessary, round to the nearest tenth.
answer attempt 1 out of 2
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Explanation:

Step1: Apply Pythagorean theorem

Let the third side be \(x\). For a right - triangle, \(a^{2}+b^{2}=c^{2}\). Here, \(c = 16\), \(b=12\), and \(a=x\). So \(x^{2}+12^{2}=16^{2}\).

Step2: Simplify the equation

\(x^{2}+144 = 256\). Then \(x^{2}=256 - 144\).
\(x^{2}=112\).

Step3: Solve for \(x\)

\(x=\sqrt{112}\). Since \(\sqrt{112}=\sqrt{16\times7}=4\sqrt{7}\approx4\times2.646 = 10.6\) (rounded to the nearest tenth).

Answer:

\(10.6\)