Question

solve for x. leave your answer in simplest radical form.
answer
attempt 1 out of 3
x =

Explanation:

Step1: Find the length of the common side

Let the common side be \( y \). Using the Pythagorean theorem \( a^{2}+b^{2}=c^{2} \) for the right - triangle with sides \( 8 \) and \( 10 \).
\( y^{2}+8^{2}=10^{2} \)
\( y^{2}=10^{2}-8^{2} \)
\( y^{2}=100 - 64 \)
\( y^{2}=36 \)

Step2: Solve for \( x \)

Now, for the right - triangle with sides \( x \), \( 5 \) and \( y = 6 \). Using the Pythagorean theorem again.
\( x^{2}+5^{2}=y^{2} \)
Since \( y^{2}=36 \), we have \( x^{2}=36 - 25 \)
\( x^{2}=11 \)
\( x=\sqrt{11} \)

Answer:

\( x = \sqrt{11} \)