Mathematics Question and Solution
Calculating r, radius of the quarter circle.
a = r+r
a = 2r units.
a is diameter.
x ~ 15
8 ~ 2r
Cross Multiply.
x = 60/r units.
b²+x² = 8²
b² = 64-(3600/r²)
b = √(64-(3600/r²)) units.
c² = r²+b²
c² = r²+√(64-(3600/r²))²
c² = r²+64-(3600/r²)
c = √((r⁴+64r²-3600)/r²)
d = r+x
d = r+(60/r)
d = (r²+60)/r units.
Calculating r.
8²+c² = d²
64+√((r⁴+64r²-3600)/r²)² = ((r²+60)/r)²
64+(r⁴+64r²-3600)/r² = (r⁴+120r²+3600)/r²
64r²+r⁴+64r²-3600 = r⁴+120r²+3600
64r²+64r²-3600 = 120r²+3600
128r²-120r² = 7200
8r² = 7200
r² = 900
r = 30 units.
Again, r is the radius of the quarter circle.
Or
15 ~ 8
a ~ d
15 ~ 8
2r ~ (r²+60)/r
Cross Multiply.
15(r²+60)/r = 16r
15r²+900 = 16r²
r² = 900
r = √(900)
r = 30 units.
Again, r is the radius of the quarter circle.
