China Gaokao 2019 Interesting Math Question

Gaokao = Baccalaureate = GCE A Level

…[Solution scrolled below]

Let Ф = 0.618

… Golden Ratio Ф = 0.618

defined as:

“Head to Throat” vs “Throat to Navel” = a/b = Ф ,

also

“Head to Navel” vs “Navel to bottom of Legs” =(a+b) / c= Ф

Knowing :

Head to Neck = 26 cm &

Legs = 105 cm

Find the height (H) ?

Note: The tricky part is to know “the neck is below the throat” & “the legs start some distance below the navel”, hence 2 inequalities :

a < 26, c > 105

H = (a + b) + c = Фc + c = (1+Ф) c = 1.618c
H > 1.618 x105
H > 169.9

H = a + b + (c)
= a + b + (a+b) / Ф
= (a+b) (1+1/Ф)
= (a +a/Ф) (1+1/Ф)
= a(1+1/Ф)(1+1/Ф)
< 26.(1+1/Ф)(1+1/Ф)

H < 178.2

ANS = H ~ 175 (B)

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