Question-25609

Question Number 25609 by behi.8.3.4.17@gmail.com last updated on 12/Dec/17

Commented by behi.8.3.4.17@gmail.com last updated on 12/Dec/17

BE = EC, AB = 12, AC = 10

parallel lines to : AE, with equal distance

from : A and B, toward C, divide the area

of A \overset{△}{B C} at ratio : 1 : 4 : 2 : 3 .

\dots \dots \dots \dots \dots \dots . . AE = ? \dots \dots \dots \dots . .

Commented by ajfour last updated on 12/Dec/17

Commented by behi.8.3.4.17@gmail.com last updated on 12/Dec/17

thanks in advance sir ajfour .

nice, smart, perfect, beautiful .

Commented by ajfour last updated on 12/Dec/17

\frac{x^{2}}{a^{2}} = \frac{1}{1 + 4} \Rightarrow a = x \sqrt{5}

\frac{{(10 - x)}^{2}}{100} = \frac{3}{3 + 2}

\Rightarrow x = 10 - 2 \sqrt{15}

s o a = 10 (\sqrt{5} - \sqrt{3})

\cos θ + \cos (180 - θ) = 0

\Rightarrow \frac{b^{2} + a^{2} - {(12)}^{2}}{2 a b} + \frac{b^{2} + a^{2} - {(10)}^{2}}{2 a b} = 0

\Rightarrow b^{2} = 122 - a^{2}

A E = b = \sqrt{122 - 100 {(\sqrt{5} - \sqrt{3})}^{2}}

= \sqrt{200 \sqrt{15} - 678} .

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