Question

Geometry: Find the value of X

Answer 1

Answer:

$x = \sqrt{30}$

Step-by-step explanation:

BD is the altitude of the right ∆ which divides the hypotenuse to create two line segments, CD, and AD.

According to the right triangle altitude theorem,

$BD = \sqrt{CD*AD}$

CD = 3, AD = 7, therefore,

$BD = \sqrt{3*7}$

$BD = \sqrt{21}$

Find x using Pythagorean theorem

$x^2 = BD^2 + CD^2$

$x^2 = (\sqrt{21})^2 + 3^2$

$x^2 = 21 + 9$

$x^2 = 30$

$x = \sqrt{30}$