Mathematics Question and Solution
2(20x)+2(30x)+2x² = (x+30)(x+20)
Where x is the radius of the inscribed circle.
It implies;
40x+60x+2x² = x²+20x+30x+600
100x+2x² = x²+50x+600
x²+50x-600 = 0
Calculating x via completing the square approach.
(x+25)² = 600+(25)²
x+25 = ±√(600+625)
x = -25±√(1225)
x = -25±35
It implies;
x = -25+35
x = 10 units.
Again, x is the radius of the inscribed circle.
Triangle height is;
x+20
= 30 units.
Triangle base is;
x+30
= 40 units.
Triangle area is;
½*base*height
= ½*40*30
= 600 square units.
