Mathematics Question and Solution
Calculating Area Red.
Let x be the side length of the ascribed square.
a = 2+3
a = 5 units.
b²+5² = x²
b = √(x²-25) units.
Calculating x.
cosc = √(x²-25)/x --- (1).
cosc = 3/x --- (2).
Equating (1) and (2).
√(x²-25)/x = 3/x
√(x²-25) = 3
x²-25 = 9
x² = 34 square units.
Where x² is the area of the square.
Calculating Shaded Red Area.
x² = 34
x = √(34) units.
Again, x is the side length of the ascribed square.
Recall.
b = √(x²-25)
And x² = 34
b = √(34-25)
b = 3 units.
It implies, red area is;
Area ascribed square - 2(area triangle with height 5 units and base 3 units).
= 34-2*½(5*3)
= 34-15
= 19 square units.
