Mathematics Question and Solution
Calculating area of the ascribed square.
a = (2+r) cm.
r is the radius of the circle yellow quarter circle.
a is AB, the side length of the ascribed square.
2(2+r)² = b²
b² = 2(4+4r+r²)
b = √(8+8r+2r²) cm.
b is BD.
r² = c²+(½(7))²
c² = r²-¼(49)
c² = ¼(4r²-49)
c = ½√(4r²-49) cm.
d = ½(b)
d = ½√(8+8r+2r²)
Calculating r.
It implies;
c = d
½√(4r²-49) = ½√(8+8r+2r²)
4r²-49 = 8+8r+2r²
2r²-8r-57 = 0
(r-2)² = ½(57)+(-2)²
(r-2)² = ½(57+8)
(r-2)² = ½(65)
r = 2±√(½(65))
Therefore;
r ≠ 2-√(½(65)) cm.
r = 2+√(½(65)) cm.
r = 7.7008771255 cm.
Again, r is the radius of the yellow inscribed quarter circle.
Recall.
a = (2+r) cm.
r is the radius of the circle yellow quarter circle.
a is AB, the side length of the ascribed square.
And r = 7.7008771255 cm.
It implies;
a = 2+7.7008771255
a= 9.7008771255 cm.
Again, a is AB, the side length of the ascribed square.
Area ascribed square is;
a²
= 9.7008771255²
= 94.107017004 cm²
