Mathematics Question and Solution
Calculating Yellow Area.
Let AB = BC = a
Let BD = b
It implies;
a² = b²+7²+2*7*bcosx
a² = b²+49+14bcosx --- (1).
a² = b²+25²-2*25*bcosx
a² = b²+625-50bcosx --- (2).
cosx = b/25 --- (3).
Equating (1) and (2).
b²+49+14bcosx = b²+625-50bcosx
49+14bcosx = 625-50bcosx
64bcosx = 576
bcosx = 576/64
bcosx = 72/8
bcosx = 9
cosx = 9/b --- (4).
Calculating b.
Equating (3) and (4).
b/25 = 9/b
b² = 9*25
b = 15 units.
cosc = 15/25
c = acos(3/5)°
d = 180-c
d = (180-acos(3/5))°
Therefore, yellow area is;
½*7*15sin(180-acos(3/5))
= 0.5*7*15*0.8
= ⅖*7*15
= 42 square units.
