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 triangle A_1 B_1 C


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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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