Answers

2014-11-07T22:00:52+08:00
Use the illustration i've made as reference. (see attachment)
taking the left right triangle, we can use Pythagorean Theorem
x^2 =  (\frac{x}{2})^2 + (x-2)^2
x^2 =  \frac{x^2}{4} + (x^2 - 4x +4)
x^2 =  \frac{x^2}{4} + x^2 - 4x + 4
multiply the whole equation with 4
4x^2 = x^2 + 4x^2 - 16x + 16
transpose all the terms from left to right, equating it to zero
0=4x^2 - 4x^2 + x^2 - 16x + 16
or
<span>4x^2-4x^2+x^2-16x+16=0
x^2 - 16x + 16 = 0
using quadratic formula
x =  \frac{-b (+-)  \sqrt{b^2-4ac} }{2a}
a = 1
b = -16
c = 16
x =  \frac{-(-16) (+-) \sqrt{(-16)^2-4(1)(16)} }{2(1)}
x =  \frac{16 (+-) \sqrt{256-64} }{2}
x = \frac{16(+-) \sqrt{192} }{2}
x = \frac{16(+-) \sqrt{64(3)} }{2}
x = \frac{16(+-) 8\sqrt{3}}{2}
x = 8 (+-) 4 \sqrt{3}
x_1 = 8 + 4 \sqrt{3}
or
x_1 = 14.9282 units
x_2 = 8 - 4\sqrt {3}
or
x_2 = 1.0718 units
therefore you can have the value of the side as 14.9282 units and/or 1.0718 units
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