Question

10.2 cm
34.5 cm
set up the problem
solution ( x=) cm (rounded to the nearest hundredths.)

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a = 10.2\) and \(b=34.5\) and hypotenuse \(x\), the Pythagorean theorem is \(a^{2}+b^{2}=x^{2}\). So, \(10.2^{2}+34.5^{2}=x^{2}\).

Step2: Calculate \(10.2^{2}\) and \(34.5^{2}\)

\(10.2^{2}=10.2\times10.2 = 104.04\)
\(34.5^{2}=34.5\times34.5=1190.25\)

Step3: Sum the results

\(104.04 + 1190.25=x^{2}\), so \(x^{2}=1294.29\)

Step4: Solve for \(x\)

\(x=\sqrt{1294.29}\approx35.98\)

Answer:

Set up the problem: \(10.2^{2}+34.5^{2}=x^{2}\)
Solution \(x = 35.98\) cm