Question

for the following 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 \(a = 8\), \(b = 12\), and \(c=x\).
So, \(x^{2}=8^{2}+12^{2}\).

Step2: Calculate \(8^{2}\) and \(12^{2}\)

\(8^{2}=64\), \(12^{2}=144\).
Then \(x^{2}=64 + 144\).

Step3: Sum the values

\(x^{2}=208\).

Step4: Solve for \(x\)

\(x=\sqrt{208}\approx14.42\)

Answer:

\(14.42\)