Difference between revisions of "2024 AMC 8 Problems/Problem 11"
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==Problem== | ==Problem== | ||
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| + | The coordinates of <math>\triangle ABC</math> are <math>A(5,7)</math>, <math>B(11,7)</math>, and <math>C(3,y)</math>, with <math>y>7</math>. The area of <math>\triangle ABC</math> is 12. What is the value of <math>y</math>? | ||
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| + | <asy> | ||
| + | |||
| + | draw((3,11)--(11,7)--(5,7)--(3,11)); | ||
| + | |||
| + | dot((5,7)); | ||
| + | label("$A(5,7)$",(5,7),S); | ||
| + | |||
| + | dot((11,7)); | ||
| + | label("$B(11,7)$",(11,7),S); | ||
| + | |||
| + | dot((3,11)); | ||
| + | label("$C(3,y)$",(3,11),NW); | ||
| + | |||
| + | </asy> | ||
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| + | |||
| + | <math>\textbf{(A) }8\qquad\textbf{(B) }9\qquad\textbf{(C) }10\qquad\textbf{(D) }11\qquad \textbf{(E) }12</math> | ||
| + | |||
==Solution 1== | ==Solution 1== | ||
The triangle has base <math>6,</math> which means its height satisfies | The triangle has base <math>6,</math> which means its height satisfies | ||
Revision as of 12:14, 26 January 2024
Contents
Problem
The coordinates of 
are 
, 
, and 
, with 
. The area of is 12. What is the value of 
?
![[asy] draw((3,11)--(11,7)--(5,7)--(3,11)); dot((5,7)); label("$A(5,7)$",(5,7),S); dot((11,7)); label("$B(11,7)$",(11,7),S); dot((3,11)); label("$C(3,y)$",(3,11),NW); [/asy]](http://latex.artofproblemsolving.com/3/a/1/3a1150ef27a4bba82b5f1aa665dc3e1dbe92d9f8.png)
Solution 1
The triangle has base 
which means its height satisfies
![\[\dfrac{6h}{2}=3h=12.\]](http://latex.artofproblemsolving.com/e/4/4/e448c160a210aadf166e977d28c622077d4e0ddf.png)
This means that 
so the answer is 
Video Solution by Math-X (First understand the problem!!!)
~Math-X
