△ABC is a right triangle with right angle C. Side AC¯¯¯¯¯¯¯¯ is 6 units longer than side BC¯¯¯¯¯¯¯¯. If the hypotenuse has length 217−−√ units, find the length of AC¯¯¯¯¯¯¯¯.

Given:

In △ABC is a right angle triangle.

AC is 6 units longer than side BC.

To find:

The length of AC.

Solution:

Let the length of BC be x.

So, Length of AC = x+6

According to the Pythagoras theorem, in a right angle triangle

△ABC is a right angle triangle and AC is hypotenuse, so

Subtract 68 from both sides.

Divide both sides by 2.

Splitting the middle term, we get

Side cannot be negative, so x=2 only.

Now,

Therefore, the length of AC is 8 units.

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step-by-step explanation: