Mathematics Question and Solution
Calculating h, height of the ascribed right-angled triangle.
Notice, 4 units is the radius of the inscribed circle.
a² = h²+40²
a= √(h²+1600) units.
a is the hypotenuse of the ascribed right-angled triangle.
Therefore;
½(4h)+½(4*40)+½(4*√(h²+1600)) = ½(40h)
4h+160+4√(h²+1600) = 40h
160+4√(h²+1600) = 36h
40+√(h²+1600) = 9h
√(h²+1600) = 9h-40
h²+1600 = (9h-40)²
h²+1600 = 81h²-720h+1600
80h²-720h = 0
80h² = 720h
8h = 72
h = 9 units.
