Mathematics Question and Solution
Calculating Square Area.
Let x be the side length of the square.
a = ½(x) units.
It implies;
b ~ ½(x)
½(x) ~ x
Cross Multiply.
bx = ¼(x²)
b = ¼(x) units.
Therefore;
c² = (¼(x))²+(½(x))²
c² = (x²/16)+(x²/4)
c = √((x²/16)+(x²/4))
c = √(5x²/16)
c = ¼√(5)x units.
c is the base of the inscribed green right-angled triangle.
d² = x²+(½(x))²
d² = x²+¼(x)²
d = √(x²+¼(x)²)
d = √(5x²/4)
d = ½√(5)x units.
d is the height of the inscribed green right-angled triangle.
Calculating x², area of the square.
½*c*d = 20
½*¼√(5)x*½√(5)x = 20
5x²/16 = 20
x² = 16*4
x² = 64 square units.
Where x, side length of the square is 8 units.
