let-ABC-be-a-escalene-triangle-of-area-7-Let-A-1-be-a-point-on-the-side-BC-and-let-B-1-and-C-1-be-points-on-the-sides-AC-and-AB-such-that-AA-1-BB-1-and-CC-1-are-parallel-Find-the-area-of-tr

Question Number 79266 by Maclaurin Stickker last updated on 24/Jan/20

l e t A B C b e a e s c a l e n e t r i a n g l e o f

a r e a 7 . L e t A_{1} b e a p o i n t o n t h e s i d e

B C, a n d l e t B_{1} a n d C_{1} b e p o i n t s o n

t h e s i d e s A C a n d A B, s u c h t h a t

{A A}_{1}, {B B}_{1} a n d {C C}_{1} a r e p a r a l l e l . F i n d

t h e a r e a o f t r i a n g l e A_{1} B_{1} C_{1} .

Commented by mr W last updated on 24/Jan/20

Δ_{A_{1} B_{1} C_{1}} = 2 Δ_{A B C}

2 \times 7 = 14

Commented by mr W last updated on 24/Jan/20

Commented by mr W last updated on 24/Jan/20

Δ_{{A B}_{1} C_{1}} = Δ_{A B C}

Δ_{{A A}_{1} B_{1}} = Δ_{{A A}_{1} B}

Δ_{{A A}_{1} C_{1}} = Δ_{{A A}_{1} C}

\Rightarrow Δ_{A_{1} B_{1} C_{1}} = 2 Δ_{A B C}

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