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# Last time I posted someone said the answer was 175, definitely wrong. Ignore dollar signs. [ACD] is the area of ACD

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In the diagram, $BD = 5$, $CE = 4$, $[ABC] = 24$, and $[ADE] = 18$. Find $[ACD]$.

Mar 16, 2020

#1
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In the diagram, BD = 5, CE = 4, [ABC] = 24, and [ADE] = 18.

Find [ACD].

$$\begin{array}{|lrcll|} \hline (1) & 24 + [ACD] &=& \dfrac{5h}{2} \\\\ (2) & 18 + [ACD] &=& \dfrac{4h}{2} \\ \hline (1)-(2): & 24 + [ACD] -(18 + [ACD]) &=& \dfrac{5h}{2}-\dfrac{4h}{2} \\\\ & 24 + [ACD] -18 - [ACD] &=& \dfrac{1h}{2} \\\\ & 24 -18 &=& \dfrac{h}{2} \\\\ & 6 &=& \dfrac{h}{2} \\\\ & \mathbf{h} &=& \mathbf{12} \\ \hline & 18 + [ACD] &=& \dfrac{4h}{2} \\ & 18 + [ACD] &=& 2h \quad & | \quad h=12 \\ & 18 + [ACD] &=& 2h \\ & 18 + [ACD] &=& 2*12 \\ & 18 + [ACD] &=& 24 \\ & [ACD] &=& 24-18 \\ & \mathbf{[ACD]} &=& \mathbf{6} \\ \hline \end{array}$$

Mar 16, 2020
#2
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Thank you for answering my question!

Guest Mar 18, 2020