Question

a triangle with side lengths 26, 18, and a right triangle inside with hypotenuse x (the image shows a triangle with a right triangle inside, labeled with 26, 18, and x as the hypotenuse of the right triangle, and there are some handwritten notes on the left side like √x etc.)

Explanation:

Step1: Identify right triangle sides

We have a right triangle with hypotenuse $26$, one leg $18$, and the other leg $x$.

Step2: Apply Pythagorean theorem

The theorem states $a^2 + b^2 = c^2$, so rearrange to solve for $x$:
$x = \sqrt{c^2 - a^2}$
Substitute $c=26$, $a=18$:
$x = \sqrt{26^2 - 18^2}$

Step3: Calculate squared values

$26^2 = 676$, $18^2 = 324$
$x = \sqrt{676 - 324}$

Step4: Compute difference and square root

$676 - 324 = 352$
$x = \sqrt{352} = \sqrt{64 \times 5.5} = 8\sqrt{11} \approx 18.76$

Answer:

$x = 8\sqrt{11}$ (or approximately $18.76$)