Question

question
the triangle below is isosceles. find the length of side ( x ) to the nearest tenth.
image of a right isosceles triangle with one leg labeled 11 and hypotenuse labeled ( x )

Explanation:

Step1: Identify triangle type

It's an isosceles right triangle, so the two legs are equal (both 11).

Step2: Apply Pythagorean theorem

The Pythagorean theorem is \( a^2 + b^2 = c^2 \), where \( a = 11 \), \( b = 11 \), and \( c = x \). Substitute values: \( x^2 = 11^2 + 11^2 \).

Step3: Calculate \( x^2 \)

\( 11^2 = 121 \), so \( x^2 = 121 + 121 = 242 \).

Step4: Solve for \( x \)

Take the square root: \( x = \sqrt{242} \approx 15.6 \) (rounded to nearest tenth).

Answer:

\( 15.6 \)