Question

find the length of side $x$ to the nearest tenth.
(right triangle with one leg 11, hypotenuse $x$, and the other leg equal in length to the first leg as indicated by the tick marks)

Explanation:

Step1: Identify triangle properties

This is an isosceles right triangle: the two legs are equal (each 11), right-angled.

Step2: Apply Pythagorean theorem

For right triangle: $a^2 + b^2 = c^2$, where $a=b=11$, $c=x$.
$$x = \sqrt{11^2 + 11^2}$$

Step3: Simplify the expression

$$x = \sqrt{2 \times 121} = 11\sqrt{2}$$

Step4: Calculate decimal value

$11\sqrt{2} \approx 11 \times 1.4142 = 15.5562$

Step5: Round to nearest tenth

Round 15.5562 to one decimal place.

Answer:

15.6