Mathematics Question and Solution
Calculating Area Yellow.
a = (3+x) units.
a is the width of the ascribed rectangle.
b = 2(7)
b = 14 units.
b is the length of the ascribed rectangle.
c = ½(a)
c = ½(3+x) units.
tany = 7/(3+x) --- (1).
tany = (0.5(3+x)/7) --- (2).
Calculating x.
It implies;
Equating (1) and (2).
½(3+x)/7 = 7/(3+x)
Cross Multiply.
49 = ½(9+6x+x²)
98 = 9+6x+x²
x²+6x-89 = 0
(x+3)² = 89+(+3)²
(x+3)² = 98
x = -3±√(98)
It implies;
x ≠ -3-7√(2)
x = (7√(2)-3) units.
x = 6.89949493661 units.
Recall.
c = ½(3+x)
And x = (7√(2)-3) units.
c = ½(3+(7√(2)-3))
c = ½(7√(2)) units.
c = 4.94974746831 units.
c is the height of the inscribed yellow area (kite).
It implies;
7√(2) ~ (7√(2)-3)
7 ~ d
Cross Multiply.
√(2)d = (7√(2)-3)
d = ½(14-3√(2)) units.
d = 4.87867965644 units.
e = 2(7-d)
e = 2(7-½(14-3√(2)))
e = (14-(14-3√(2)))
e = 3√(2) units.
e = 4.24264068712 units.
e is the width of the inscribed yellow area (kite).
Therefore, area yellow is;
½(c*e)
= ½*½(7√(2))*3√(2)
= ½(21) square units.
= 10.5 square units.
