Mathematics Question and Solution
Calculating Area Blue.
Let x be the base of the inscribed white right-angled triangle with hypotenuse 10 units.
a² = 10²+10²
a = √(2(10²))
a = 10√(2) units.
a is the hypotenuse of the ascribed right-angled triangle.
b+90+135 = 360
b = 360-90-135
b = 270-135
b = 135°
Notice.
The two inscribed blue scalene triangles are similar (they both have equal positions interior angles).
It implies;
10 ~ 10√(2)
x ~ c
Cross Multiply.
10c = 10√(2)x
c = √(2)x units.
Again.
10 ~ 10√(2)
√(2)x ~ d
Cross Multiply.
10d = 20x
d = 2x units.
d is the height of the inscribed white right-angled triangle with hypotenuse 10 units.
Therefore, calculating x.
x²+(2x)² = 10²
5x² = 100
x² = 100/5
x = √(20)
x = 2√(5) units.
Recall.
d = 2x units.
And x = 2√(5) units.
d = 2*2√(5)
d = 4√(5) units.
Again, d is the height of the inscribed white right-angled triangle with hypotenuse 10 units.
It implies, area blue is;
Area triangle with height and base 10 units respectively - Area triangle with height 4√(5) units and base 2√(5) units.
= (0.5*10*10)-(0.5*4√(5)*2√(5))
= 50-20
= 30 square units.
