Mathematics Question and Solution
Calculating Area Rectangle.
Let BC be x.
a²+x² = 15²
a² = 225-x²
a = √(225-x²) units.
a is CD.
15 ~ x
5 ~ b
Cross Multiply.
b = x/3 units.
15 ~ √(225-x²)
5 ~ c
Cross Multiply.
c = ⅓√(225-x²) units.
d = x+b
d = x+(x/3)
d = ⅓(4x) units.
e = a+c
e = √(225-x²)+⅓√(225-x²)
e = ⅓(4√(225-x²)) units.
f = 15+5
f = 20 units.
f is BE.
g² = (⅓(4√(225-x²)))²+(x/3)²
g² = ⅑(3600-16x²)+(x²/9)
g² = 400-⅑(16x²)+(x²/9)
g² = 400-⅑(15x²)
g² = ⅑(3600-15x²)
g = ⅓√(3600-15x²) units.
g is CE.
It implies;
⅓√(3600-15x²) ~ 20
√(225-x²) ~ x
Cross Multiply.
x√(3600-15x²) = 60√(225-x²)
x²(3600-15x²) = 3600(225-x²)
3600x²-15x⁴ = 810000-3600x²
15x⁴-7200x²+810000 = 0
5x⁴-2400x²+270000 = 0
x⁴-480x²+54000 = 0
It implies;
x = 6√(5) units.
Again, x is BC.
Calculating a.
a = √(225-x²)
And x = 6√(5) units.
a = √(225-(6√(5))²)
a = √(225-180)
a = √(45)
a = 3√(5) units.
Again, a is CD.
Therefore, Area Rectangle is;
BC * CD
= x * a
= 6√(5)*3√(5)
= 18*5
= 90 square units.
