civonamzuk

This is very simple.

Δ ABC ~ Δ ACD

3 / 6 = 6 / BD

BD = 12

AB = √225

9 - biology

5 - chemistry

7 - ONLY biology

3 - ONLY chemistry

2 - BOTH: biology and chemistry

[ABC] = 25

Triangles ABC and ACD are the right-angled triangles.

Angle B = 42º

∠GAF = ∠HCD = ∠JEF = 45º

HC = √2

JE = √72 / 10

HC / JE = 5/3

Let's see who's right: guest 1, or guest 2

7/14 = (14 - YZ) / 7

49 = 196 - 14(YZ)

14(YZ) = 147

YZ = 10.5  

Angle D = 51.42857143 degrees 

Angle D = 1/2(180 - 3*∠B)

∠B = 1/7(180)

(Read from the bottom up )

Hint:  find the height and then use this formula:  V = 1/3 h (a² + ab + b²)

BP = sqrt(AB² + AP²)

PT = sqrt(BP² - BT²)

BD = sqrt(DC² / 2)