Question

solve for x. leave your answer in simplest radical form.

Explanation:

Step1: Adjust the figure to a right triangle

We can consider the vertical side difference: \( 3 - 1 = 2 \), and the horizontal side is \( 3 \). Now we have a right triangle with legs \( 3 \) and \( 2 \), and hypotenuse \( x \).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem states that for a right triangle with legs \( a \) and \( b \), and hypotenuse \( c \), \( a^{2}+b^{2}=c^{2} \). Here, \( a = 3 \), \( b = 2 \), so \( x^{2}=3^{2}+2^{2} \).

Step3: Calculate the value of \( x^{2} \)

\( 3^{2}+2^{2}=9 + 4=13 \), so \( x^{2}=13 \).

Step4: Solve for \( x \)

Taking the square root of both sides, \( x=\sqrt{13} \) (since length can't be negative).

Answer:

\( \sqrt{13} \)