Mathematics Question and Solution
Calculating perimeter of the blue inscribed square.
5² = 7²+8²-2*7*8cosa
112cosa = 49+64-25
cosa = 88/112
a = acos(11/14)
a = 38.2132107017°
5/sin38.2132107017 = 7/sinb
sinb = ⅕(7sin38.2132107017)
sinb = 0.86602540378
b = asin(0.86602540378)
b = 60°
c = 180-60
c = 120°
d = 180-120-38.2132107017
d = 21.7867892983°
Calculating x, side length of the inscribed blue square.
x/sin21.7867892983 = 7/sin120
x = (7sin21.7867892983)/(sin120)
x = 3 units.
There, perimeter of the inscribed blue square is;
4x
And x = 3 units.
= 4*3
= 12 units.
