Question

use the observation you made in slide 10 to find the value of x. show your work in the sketch area.
(image of a right triangle with segments 40, 49, and x, and right angles marked)

Explanation:

Step1: Identify similar triangles property

When an altitude is drawn to the hypotenuse of a right triangle, the length of the hypotenuse is equal to $\frac{\text{length of leg}^2}{\text{adjacent segment of hypotenuse}}$.

Step2: Substitute given values

Here, leg length = 49, adjacent segment = 40.
$$x = \frac{49^2}{40}$$

Step3: Calculate the value

$$x = \frac{2401}{40} = 60.025$$

Answer:

$60.025$ or $\frac{2401}{40}$