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Anna71 [15]
2 years ago
10

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?

Mathematics
2 answers:
ozzi2 years ago
6 0

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.

makvit [3.9K]2 years ago
6 0

Answer:

15, 20

Step-by-step explanation:

Just cause

(Tales Theorem)

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