Mathematics Question and Solution
Calculating x.
a² = 6²+x²
a = √(36+x²) units.
a is the diagonal of the rectangle.
b = ½(a)
b = ½√(36+x²) units.
Therefore, length x, the width of the rectangle is;
6 ~ ½√(36+x²)
x ~ 2
Cross Multiply.
12 = ½(x√(36+x²))
24 = x√(36+x²)
24² = x²(36+x²)
576 = 36x²+x⁴
x⁴+36x²-576 = 0
x⁴+48x²-12x²-576 = 0
x²(x²+48)-12(x²+48) = 0
(x²-12)(x²+48) = 0
It implies;
x²+48 = 0
x² ≠ -48
Again;
x²-12 = 0
x² = 12
x = √(12)
x = 2√(3) units.
Or
A smart approach is;
x = √(2*6)
x = √(12)
x = 2√(3) units.
