Difference between revisions of "2019 AMC 8 Problems/Problem 21"
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==Solution 1== | ==Solution 1== | ||
| − | You need to first find the coordinates where the graphs intersect. <math>y=5</math>, and <math>y=x+1</math> intersect at <math>(4,5)</math>. <math>y=5</math>, and <math>y=1-x</math> intersect at <math>(-4,5)</math>. <math>y=1-x</math> and <math>y=1+x</math> intersect at <math>(1,0)</math>. Using the [[Shoelace Theorem]] you get < | + | You need to first find the coordinates where the graphs intersect. <math>y=5</math>, and <math>y=x+1</math> intersect at <math>(4,5)</math>. <math>y=5</math>, and <math>y=1-x</math> intersect at <math>(-4,5)</math>. <math>y=1-x</math> and <math>y=1+x</math> intersect at <math>(1,0)</math>. Using the [[Shoelace Theorem]] you get <math></math>\left(\frac{(20-4)-(-20+4)}{2}\right)<math>=</math><math>\frac{32}{2} </math>=<math> \boxed{\textbf{(E)}\ 16}</math>.~heeeeeeheeeee |
==Solution 2== | ==Solution 2== | ||
Revision as of 13:33, 23 November 2019
Contents
Problem 21
What is the area of the triangle formed by the lines 
, 
, and 
?
Solution 1
You need to first find the coordinates where the graphs intersect. , and 
intersect at 
. , and intersect at 
. and intersect at 
. Using the Shoelace Theorem you get $$ (Error compiling LaTeX. Unknown error_msg)\left(\frac{(20-4)-(-20+4)}{2}\right)
=
.~heeeeeeheeeee
Solution 2
Graphing the lines, we can see that the height of the triangle is 4, and the base is 8. Using the formula for the area of a triangle, we get 
which is equal to . ~SmileKat32
See Also
| 2019 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 20 |
Followed by Problem 22 | |
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
