Mathematics Question and Solution
Let the centre of the semi circle be O.
Let d be 2a.
It implies, a is the radius of the semi circle.
a = OA = OB
(2a)² = b²+7²
b² = 4a²-49
b = √(4a²-49) units.
c = ½(b)
c = ½√(4a²-49) units.
e = ½(AD)
e = ½(7)
e = 3.5 units.
f = a-e
f = (a-3.5) units.
Calculating a.
It implies;
15² = (a-3.5)²+(½√(4a²-49))²
225 = a²-7a+(49/4)++a²-(49/4)
225 = 2a²-7a
2a²-7a-225 = 0
Resolving the above quadratic equation via factorization approach.
2a²-25a+18a-225 = 0
a(2a-25)+9(2a-25) = 0
(2a-25)(a+9) = 0
2a-25 = 0
Or
a+9 = 0
It implies;
a ≠ -9
a = (25/2) units.
a = 12.5 units.
Again, a is the radius of the half circle.
Therefore, d, diameter of the half circle is;
d = 2a
And a = 12.5 units.
d = 2*12.5
d = 25 units.
