Question

in the figure below, d is the mid - point of ac, and bd is perpendicular to ac. what is the length of bd? 15 centimeters 16 centimeters 18 centimeters 20 centimeters

Explanation:

Step1: Find length of AD

Since D is the mid - point of AC and AC = 30 cm, then $AD=\frac{AC}{2}=\frac{30}{2}=15$ cm.

Step2: Apply Pythagorean theorem in right - triangle ABD

In right - triangle ABD, let AB = 25 cm and AD = 15 cm. According to the Pythagorean theorem $AB^{2}=AD^{2}+BD^{2}$, so $BD=\sqrt{AB^{2}-AD^{2}}$.

Step3: Calculate BD

$BD=\sqrt{25^{2}-15^{2}}=\sqrt{(25 + 15)(25 - 15)}=\sqrt{40\times10}=\sqrt{400}=20$ cm.

Answer:

D. 20 centimeters