Mathematics Question and Solution
Let a be the radius of the quarter circle.
b = (a-7) units.
c = (a-14) units.
It implies;
a² = (a-7)²+(a-14)²
a² = a²-14a+49+a²-28a+196
a²-42a+245 = 0
Resolving the above quadratic equation a via factorization approach to get a.
a²-35a-7a+245 = 0
a(a-35)-7(a-35) = 0
(a-35)(a-7) = 0
It implies;
a = 35 units.
Again, a is the radius of the quarter circle.
Recall.
b = a-7
And a = 35 units.
b = 35-7
b = 28 units.
c = a-14
And a = 35 units.
c = 35-14
c = 21 units.
Pink Area is;
Area quarter circle with radius 35 units - Area rectangle with length 28 units and base 21 units.
= ¼(35²)π-(28*21)
= ¼(1225π)-588
= ¼(1225π-2352) square units.
= 374.1127501619 square units.
