Question

the diagram shows the parts of a right triangle with an altitude to the hypotenuse. for the two given measures, find the other four.$h=26, s_1=13LXB0a = \squareLXB1u_2 = \square$(simplify your answers. type exact answers, using radicals as needed.)

Explanation:

Step1: Find $u_1$ (geometric mean)

In a right triangle, the leg $u_1$ is the geometric mean of the hypotenuse $h$ and the adjacent segment $s_1$.
$$u_1 = \sqrt{h \times s_1} = \sqrt{26 \times 13} = \sqrt{338} = 13\sqrt{2}$$

Step2: Calculate $s_2$

Subtract $s_1$ from hypotenuse $h$.
$$s_2 = h - s_1 = 26 - 13 = 13$$

Step3: Find $u_2$ (geometric mean)

The leg $u_2$ is the geometric mean of $h$ and $s_2$.
$$u_2 = \sqrt{h \times s_2} = \sqrt{26 \times 13} = 13\sqrt{2}$$

Step4: Find altitude $a$ (geometric mean)

The altitude $a$ is the geometric mean of $s_1$ and $s_2$.
$$a = \sqrt{s_1 \times s_2} = \sqrt{13 \times 13} = 13$$

Answer:

$s_2 = 13$
$a = 13$
$u_1 = 13\sqrt{2}$
$u_2 = 13\sqrt{2}$