Mathematics Question and Solution
Let length AB be x.
A careful analysis carried out on the given composite plane shape lead to the derivation of right-angled tiangle EQX with hypotenuse QX ⅓(4x) and the two adjacent side of the triangle, EQ ⅔(√(3))x and EX (x-1) respectively.
Therefore applying Pythagoras rule to get x (length AB).
(⅔(√(3))x)² + (x-1)² = (⅓(4x))²
(12x²)/9 + x² - 2x + 1 = (16x²)/9
21x² - 18x + 9 = 16x²
5x² - 18x + 9 = 0
Resolving the above quadratic equation via factorization approach.
(5x²-15x)-(3x+9) = 0
5x(x-3)-3(x-3)=0
(5x-3)(x-3)=0
Therefore;
x ≠ 0.6
x = 3 units.
It implies;
Length AB exact is
= 3 unit.
Or
x can also be;
Sin30=(x-1)/(⅓(4x))
½=(x-1)/(⅓(4x))
2x-2=⅓(4x)
6x-6=4x
2x=6
x = 3 unit.
