Answer:
5
Step-by-step explanation:
∆FGH is similar to ∆JKH. Therefore, their corresponding lengths are proportional to one another. Thus:
[tex] \frac{GH}{KH} = \frac{FH}{JH} [/tex]
GH = x + 15
KH = x
FH = 12 + 4 = 16
JH = 4
Plug in the values
[tex] \frac{x + 15}{x} = \frac{16}{4} [/tex]
Cross multiply
[tex] (x + 15) \times 4 = 16 \times x [/tex]
[tex] 4x + 60 = 16x [/tex]
Subtract 4x from each side
[tex] 60 = 16x - 4x [/tex]
[tex] 60 = 12x [/tex]
Divide both sides by 12
x = 5
KH = x = 5
