Mathematics Question and Solution
Calculating x.
a² = 24²+x²
a = √(x²+576) units.
a is the diameter of the ascribed circle.
b = ½(a)
b = ½√(x²+576) units.
b is the radius of the circle.
c = (x-11) units.
d = ½√(x²+576)-7+½√(x²+576)
d = (√(x²+576)-7) units.
Calculating x.
7*(√(x²+576)-7) = 11*(x-11)
7√(x²+576)-49 = 11x-121
7√(x²+576) = 11x-72
49(x²+576) = 121x²-1584x+5184
49x²+28224 = 121x²-1584x+5184
72x²-1584x-23040 = 0
9x²-198x-2880 = 0
x²-22x-320 = 0
(x-11)² = 320+(11)²
(x-11)² = 320+121
x = 11±√(441)
x = 11±21
Therefore;
x ≠ 11-21
x = 11+21
x = 32 units.
