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# help plz

+1
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We have a triangle $$\triangle ABC$$ and a point $$K$$ on segment $$\overline{BC}$$ such that $$AK$$ is an altitude to $$\triangle ABC$$. If $$AK = 6,$$ $$BK = 8$$, and $$CK = 6,$$ then what is the perimeter of the triangle?

Dec 18, 2018

### Best Answer

#1
+7220
+2

First thing we know BC = BK + CK = 14.

Then we use Pythagorean theorem twice to get:

$$AB = \sqrt{AK^2 + BK^2} = 10$$

$$AC = \sqrt{AK^2+CK^2} = 6\sqrt2$$

Therefore,

Perimeter = AB + AC + BC = 14 + 10 + 6√2 = 24 + 6 √ 2

Dec 18, 2018

### 1+0 Answers

#1
+7220
+2
Best Answer

First thing we know BC = BK + CK = 14.

Then we use Pythagorean theorem twice to get:

$$AB = \sqrt{AK^2 + BK^2} = 10$$

$$AC = \sqrt{AK^2+CK^2} = 6\sqrt2$$

Therefore,

Perimeter = AB + AC + BC = 14 + 10 + 6√2 = 24 + 6 √ 2

MaxWong Dec 18, 2018

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