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
[tex]\frac{2}{HK} = \frac{HK}{8}[/tex]
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
Read more about similar triangles at:
https://brainly.com/question/14285697
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