Mathematics Question and Solution
a² = (3+5)²+x²
a² = a²-64
a = √(64+x²) cm.
b = (8-x) cm.
It implies;
5 ~ 8
(8-x) ~ √(64+x²)
Cross Multiply.
8(8-x) = 5√(64+x²)
(64-8x)² = 25(64+x²)
4096-1024x+64x² = 1600+25x²
2496-1024+39x² = 0
Resolving the above quadratic equation.
x = 2.71909 cm.
Therefore;
(8-2.71909)² = 5²+c²
c = 1.69941473105 cm.
Recall.
a = √(64+x²)
And x = 2.71909 cm.
a = √(64+(2.71909)²)
a = 8.44946450541 cm.
d = a+c
d = 8.44946450541+1.69941473105
d = 10.1488792365 cm.
e = d-6
e = 4.1488792365 cm.
Therefore, Area Blue is;
Area triangle with height 5 cm and base 10.1488792365 cm + Area triangle with height and base 8 cm respectively - Area triangle with height 5 cm and base 8 cm - Area triangle with height 5 cm and base 4.1488792365 cm.
= ½(5*10.1488792365)+½(8*8)-½(5*8)-½(5*4.1488792365)
= 27 cm²
Or
Blue Area is;
½(5*6)+½(8*3)
= ½(30+24)
= ½(54)
= 27 cm²
