Question-187819

Question Number 187819 by normans last updated on 22/Feb/23

Answered by mr W last updated on 22/Feb/23

Commented by mr W last updated on 22/Feb/23

a = 10

b = 8

\cos α = \frac{2 c}{a + b}

{E D}^{2} = a^{2} + c^{2} - 2 a c \times \frac{2 c}{a + b}

{B D}^{2} = a^{2} + 4 c^{2} - 4 a c \times \frac{2 c}{a + b}

{E D}^{2} + {B D}^{2} = c^{2}

a^{2} + c^{2} - 2 a c \times \frac{2 c}{a + b} + a^{2} + 4 c^{2} - 4 a c \times \frac{2 c}{a + b} = c^{2}

c^{2} = \frac{a^{2} (a + b)}{2 (2 a - b)}

\Rightarrow c = a \sqrt{\frac{a + b}{2 (2 a - b)}}

B C = \sqrt{{(a + b)}^{2} - {(2 c)}^{2}} = \sqrt{\frac{b (a^{2} - b^{2})}{2 a - b}}

a r e a o f t r i a n g l e A B C :

Δ = \frac{(2 c) \times B C}{2} = a \sqrt{\frac{a + b}{2 (2 a - b)}} \sqrt{\frac{b (a^{2} - b^{2})}{2 a - b}}

Δ = \frac{a (a + b)}{2 a - b} \sqrt{\frac{b (a - b)}{2}}

Δ = \frac{10 \times 18}{12} \sqrt{\frac{8 \times 2}{2}} = 30 \sqrt{2} ✓

Commented by normans last updated on 22/Feb/23

n i c e s o l u t i o n, t h a n k y o u s i r

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