Mathematics Question and Solution
Let a be the side length of the inscribed square.
Calculating a², area of the inscribed square.
tan60 = a/b
b = ⅓(√(3)a) cm.
tan30 = a/c
c = √(3)a cm.
Calculating a.
It implies;
b+a+c = 13
⅓(√(3)a)+a+√(3)a = 13
(4√(3)+3)a = 39
a = (39(4√(3)-3))/39
a = (4√(3)-3) cm.
It implies;
a²
= (4√(3)-3)²
= 48-24√(3)+9)
= (57-24√(3)) cm²
= 3(19-8√(3)) cm²
= 15.4307806183 cm²
Again, a² is the area of the inscribed square.
