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What are HK and GH?

A. HK = 5 GH = V29
B. HK=4 GH=2\5
C. HK = 2V5 GH=2v6
D. HK = V5 GH=3

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The triangles are similar triangles, and the values of HK and GH are (b) 4 and 2√5, respectively

How to determine the length HK?

The triangles are similar triangles, and they are represented by the following similarity ratio:

GK : HK = HK : JK

From the question, we have:

GK = 2 and JK = 8

So, we have:

2 : HK = HK : 8

Express as fractions

$$\frac{2}{HK} = \frac{HK}{8}$$

Cross multiply

HK² = 16

Take the positive square root of both sides

HK = 4

The length GH is calculated using the following Pythagoras theorem

GH² = GK² + HK²

This gives

GH² = 2² + 4²

Evaluate the squares

GH² = 20

Solve for GH

GH = 2√5

Hence, the values of HK and GH are (b) 4 and 2√5, respectively