Mathematics Question and Solution
Calculating Area BCDA, Area of the Ascribed Square.
Notice.
Length EF = 1 cm.
Let x be the FD, the radius of the congruent circles.
a² = 2x²
a = √(2)x cm.
b = ½(a)
b = ½√(2)x cm.
c = x+b
c = (x+½√(2)x) cm.
Calculating x.
1² = c²+b²
1 = (x+½√(2)x)²+(½√(2)x)²
1 = x²+√(2)x²+½(x²)+½(x²)
1 = x²+√(2)x²+x²
1 = 2x²+√(2)x²
1 = (2+√(2))x²
x² = 1/(2+√(2))
x = √(1/(2+√(2)))
x = 0.54119610015 cm.
Again, x is FD, the radius of the congruent circles.
AB = 2(FD)
FD = FC = x
AB = 2x
AB = 2(0.54119610015)
AB = 1.0823922003 cm.
AB = CD, the width of the ascribed rectangle.
Recall.
c = (x+½√(2)x)
And x = 0.54119610015 cm.
c = 0.54119610015+0.5√(2)*0.54119610015
c = 0.92387953252 cm.
BC = 2c
BC = 2*0.92387953252
BC = 1.84775906504 cm.
BC = AD, the length of the ascribed rectangle.
Therefore, Area BCDA (Area ascribed rectangle) is;
AB*BC
= 1.0823922003*1.84775906504
= 2 cm²
