Question

An altitude of a right triangle to its hypotenuse divides this hypotenuse into two segments that measure 9cm, and 16cm. What are the lengths of the legs of this triangle?

Answer 1

Answer:

Step-by-step explanation:

Let a be the length of the altitude, then from the given triangles, applying the basic proportionality theorem,  we get

$\frac{BD}{AD}=\frac{DC}{BD}$

⇒$(BD)^{2}=DC{\times}AD$

⇒$(BD)^2=9{\times}16$

⇒$BD=\sqrt{144}$

⇒$BD=12 cm$

Thus, the length of altitude is: 12 cm.

Now, $\frac{AB}{AD}=\frac{AC}{AB}$

⇒$(AB)^{2}=220$

⇒$AB= 14.83 cm$

Also, $\frac{BC}{DC}\frac{AC}{BC}$

⇒$(BC)^{2}=400$

⇒$BC=20 cm$

Thus, the lengths of the legs of this triangle are 14.83 and 20 cm.

Answer 2

Answer:

15, 20

Step-by-step explanation:

Just cause

(Tales Theorem)