# In a right-angled triangle with leg 9, the length of the height drawn to the hypotenuse is 18.

September 20, 2021 | education

| **In a right-angled triangle with leg 9, the length of the height drawn to the hypotenuse is 18. Find the length of the hypotenuse.**

Given:

Right-angled triangle ABC,

AC = 9√5,

CK – height,

CK = 18.

Find the length of the hypotenuse AB -?

Solution:

1) Consider the triangle ACK according to the Pythagorean theorem:

AK² = (9√5) ² – 18²;

AK² = 405 – 324;

AK² = 81;

AK = 9.

2) Consider the ABC triangle:

CK² = AK · KB;

18² = 9 · BK;

324 = 9 BK;

BK = 324: 9;

BK = 36

3) AB = AK + BK = 9 + 36 = 45.

Answer: 45.

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