Mathematics Question and Solution
Calculating area A (Area of one of the two inscribed equal squares).
Let their side length be x each.
a = 4+9
a = 13 units.
b = x+x
b = 2x units.
c²+4² = (2x)²
c = √(4x²-16) units.
d = 2c
d = 2√(4x²-16) units.
It implies;
e ~ x
4 ~ 2x
Cross Multiply.
2ex = 4x
e = 2 units.
f = ½(c)
f = ½√(4x²-16) units.
g = c-2
g = (√(4x²-16)-2) units.
tanh = 13/(2√(4x²-16)) --- (1).
tanh = (½√(4x²-16))/(√(4x²-16)-2)
tanh = = √(4x²-16)/(2√(4x²-16)-4) --- (2).
Equating (1) and (2).
13/(2√(4x²-16)) = √(4x²-16)/(2√(4x²-16)-4)
2(4x²-16) = 26√(4x²-16)-52
8x²-32 = 26√(4x²-16)-52
8x²+20 = 26√(4x²-16)
4x²+10 = 13√(4x²-16)
(4x²+10)² = 169(4x²-16)
16x⁴+80x²+100 = 676x²-2704
16x⁴-596x²+2804 = 0
4x⁴-149x²+701 = 0 --- (3).
At (3).
Calculating Area A.
(x²-(149/8))² = (-701/4)+(-149/8)²
(x²-(149/8))² = 10985/64
x²-(149/8) = ±√(10985/64)
x² = (149/8)±(13√(65)/8)
It implies;
x² ≠ ⅛(149-13√(65)) square units.
x² = ⅛(149-13√(65)) square units.
x² = 31.726168841 square units.
Where x² is area A.
