Mathematics Question and Solution
Calculating Area Red.
a = (2x+6) cm.
a is the height of the ascribed right-angled triangle.
b = (9x+6) cm.
b is the base of the ascribed right-angled triangle.
c = 13x cm.
c is the hypotenuse of the ascribed right-angled triangle.
Calculating x.
c² = a²+b²
(13x)² = (2x+6)²+(9x+6)²
169x² = 4x²+24x+36+81x²+108x+36
84x² = 132x+72
21x²-33x-18 = 0
7x²-11x-6 = 0
7x²-14x+3x-6 = 0
7x(x-2)+3(x-2) = 0
(7x+3)(x-2) = 0
It Implies;
x ≠ -3/7
x = 2 cm.
Recall.
a = (2x+6) cm.
And x = 2 cm.
a = 2*2+6
a = 10 cm.
b = (9x+6) cm.
And x = 2 cm.
b = 9*2+6
b = 24 cm.
Area Red is;
(½*10*24)-(½*4*18)
= 120-36
= 84 cm²
