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If FI= 6, IH=12, calculate the length of GI

1. 8
2. 6√2
3. 12
4. 10​

If FI= 6, IH=12, calculate the length of GI 1. 8 2. 6√2 3. 12 4. 10​-example-1
User Rabsom
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7.5k points

1 Answer

6 votes

Answer:

2. 6√2

Explanation:

You want the measure of altitude GI that divides the hypotenuse of right triangle FGH into the parts FI=6 and IH=12.

Geometric mean

The altitude of the triangle is the geometric mean of the lengths of the hypotenuse segments:

GI = √(FI·IH)

GI = √(6·12) = 6√2

The length of GI is 6√2.

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Additional comment

This relation is based on the fact that all of the triangles are similar. The ratios of short to long sides are ...

FI/GI = GI/IH

GI² = FI·IH . . . . . . . cross multiply

GI = √(FI·IH) . . . . . take the square root

The two other geometric mean relations in this geometry are ...

FG = √(FI·FH

HG = √(HI·HF)

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User Michael L
by
8.3k points

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