2024 SSMO Relay Round 1 Problems/Problem 1

Problem

Let $AD$ be an altitude of triangle $ABC$ and let $DE$ be an altitude of triangle $ACD.$ If $AB=29,CE=9,$ and $DE=12,$ what is the area of triangle $ABC?$

$[asy] size(200); pair A,B,C,D,EE; A = (0,20); B = (-21,0); C = (15,0); D = (0,0); EE = 0.36*A+0.64*C; draw(A--B--C--cycle); draw(A--D--EE); dot("$A$", A, N); dot("$B$", B, W); dot("$C$", C, E); dot("$D$", D, S); dot("$E$", EE, dir(EE)); [/asy]$

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2024 SSMO Relay Round 1 Problems/Problem 1

Problem

Solution