Mathematics Question and Solution
Calculating area of the ascribed square.
Let x be each of the two equal lengths.
a = 2x units.
a is the side length of the ascribed square.
tanb = 2x/x
b = atan(2)°
c = 180-45-atan(2)
c = (45+atan(½))°
(x/sin(45+atan(½))) = (d/sin45)
d = 0.7453559925x units.
d is the adjacent base of the blue inscribed triangle.
cos(atan(½)) = x/e
e = 1.11803398875x units.
e is the adjacent height of the blue inscribed triangle.
Calculating x.
0.5*d*e = 10
0.7453559925x*1.11803398875x = 20
0.83333333333x² = 20
⅚(x²) = 20
5x² = 120
x² = 24
x = √(24)
x = 2√(6) units.
Recall.
a = 2x units.
a is the side length of the ascribed square.
And x = 2√(6) units.
a = 2*2√(6)
a = 4√(6) units.
Are ascribed square is;
a²
= (4√(6))²
= 16*6
= 96 square units.
