2018 AMC 8 Problems/Problem 20
Contents
Problem 20
In 
a point 
is on 
with 
and 
Point 
is on 
so that 
and point 
is on 
so that 
What is the ratio of the area of 
to the area of 
![[asy] size(7cm); pair A,B,C,DD,EE,FF; A = (0,0); B = (3,0); C = (0.5,2.5); EE = (1,0); DD = intersectionpoint(A--C,EE--EE+(C-B)); FF = intersectionpoint(B--C,EE--EE+(C-A)); draw(A--B--C--A--DD--EE--FF,black+1bp); label("$A$",A,S); label("$B$",B,S); label("$C$",C,N); label("$D$",DD,W); label("$E$",EE,S); label("$F$",FF,NE); label("$1$",(A+EE)/2,S); label("$2$",(EE+B)/2,S); [/asy]](http://latex.artofproblemsolving.com/0/5/7/0571cfd5e8f21ce8031af38df8ba2295bdf2449a.png)
==Solution 1==fdsdfghjk./.lkjhyt5r4e3w2qqasxdcfvgbhnjm,./ pooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooop
Solution 2
We can extend it into a parallelogram, so it would equal 
. The smaller parallelogram is 1 a times 2 b. The smaller parallelogram is $o0i9u8y7t6r5e4sdrftgyhujik,l.;koiju87y6
by poooooopoooooopopoooopopop
Solution 3
. We can substitute 
as 
and 
as 
, where 
is . Side 
having, distance 
, has 
parts also. Anbe 
. Parallelogram to $\triangle{ABC}= \frac{2z}{4.5z}=\frac{2}{4.5}=9iuytrewdrfghnjkmjhuytrdefgbhn \frac{4}{9}}$ (Error compiling LaTeX. Unknown error_msg).
rfedswedfvgb by theultimatepooooooper
See Also
| 2018 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 19 |
Followed by Problem 21 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
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