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?

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kutakana kutakana · Answer 1 · 2019-02-19T01:05:46+01:00

Answer:

20 and 15

Step-by-step explanation:

9+16=25

√9(25)=√225=15

√16(25)=√400=20

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sheenuvt12 sheenuvt12 · Answer 2 · 2022-06-10T19:55:08+02:00

The lengths of the legs of this triangle are 20 cm and 15 cm respectively.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the altitude, and 'y' and 'z' represents the two legs.

Then, applying Pythagoras theorem

y² =x² + 9²

x² = y² - 9²...............(1)

and,

z² = x² + 16²

x² = z² - 16².........................(2)

Comparing (1) and (2), we get

y² - 9² = z² - 16²

y² = z² - 16² + 9² (3)

From the triangle:

(9 + 16)² = y² + z²

25² = (z² - 16² + 9²) + z²

z= 20 cm

and, y² = (20)² - 16² + 9²

y= 15 cm

Hence, The lengths of the legs of this triangle are 20 cm and 15 cm respectively.

Learn more about equation here:

brainly.com/question/2972832

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