Mathematics Question and Solution
Calculating Area Red.
Let x be the radius of the circle.
a = (x-7) cm.
Calculating x.
x²+(x-7) = 13²
x²+x²-14x+49 = 169
2x²-14x-120 = 0
x²-7x-60 = 0
x²-12x+5x-60 = 0
x(x-12)+5(x-12) = 0
(x-12)(x+5) = 0
It implies;
x ≠ -5
x = 12 cm.
Again, x is the radius of the circle.
Recall.
a = x-7
And x = 12 cm.
a = 12-7
a = 5 cm.
Therefore, area red is ;
Area quarter circle with radius 12 cm - Area right-angled triangle with height 12 cm and base 5 cm.
(¼*12²π) - (½*12*5)
= 36π-30
= 6(6π-5) cm²
