Question

ng right triangle, find the side length x. round your answer to the nearest hundredth.

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Let \(a = 16\), \(c=20\), and \(b=x\). Then \(x^{2}+16^{2}=20^{2}\).

Step2: Rearrange the formula to solve for \(x\)

\(x^{2}=20^{2}-16^{2}\).
Calculate \(20^{2}=400\) and \(16^{2}=256\). So \(x^{2}=400 - 256=144\).

Step3: Find the value of \(x\)

Take the square root of both sides: \(x=\sqrt{144}\). But wait, we made a mistake above. The correct formula is \(x=\sqrt{20^{2}-16^{2}}=\sqrt{(20 + 16)(20 - 16)}\) (using \(a^{2}-b^{2}=(a + b)(a - b)\)).
\(x=\sqrt{(20 + 16)(20 - 16)}=\sqrt{36\times4}=\sqrt{144}=12\) (exact value, no rounding needed as it's an integer).

Answer:

\(12\)