2024 AMC 8 Problems/Problem 11

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Problem

The coordinates of $\triangle ABC$ are $A(5,7)$, $B(11,7)$, and $C(3,y)$, with $y>7$. The area of $\triangle ABC$ is 12. What is the value of $y$?

[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]


$\textbf{(A) }8\qquad\textbf{(B) }9\qquad\textbf{(C) }10\qquad\textbf{(D) }11\qquad \textbf{(E) }12$

Solution 1

The triangle has base $6,$ which means its height satisfies \[\dfrac{6h}{2}=3h=12.\] This means that $h=4,$ so the answer is $7+4=\boxed{(D) 11}$

Video Solution by Math-X (First understand the problem!!!)

https://youtu.be/LBcftVLvynE

~Math-X

Video Solution (easy to digest) by Power Solve

https://www.youtube.com/watch?v=2UIVXOB4f0o