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mamaluj [8]
3 years ago
15

If line y bisects AC, AB = 4-5x, and BC =2x+25, AC

Mathematics
1 answer:
jolli1 [7]3 years ago
7 0
4 - 5x = 2x + 25
4 = 7x + 25
-21 = 7x
-3 = x

4 - 5x + 2x + 25 = ac
4 - 5(-3) + 2(-3) + 25 = ac
4 - (-15) + (-6) + 25 = ac
19 + (-6) + 25 = ac
38 = ac
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Why is ac smaller than ad if they both look very close
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Let's begin by listing out the information given to us:

We start out by observing that Triangles MKR & ACD are similar or proportional

\begin{gathered} MK=21;AC=\text{?} \\ MR=24;AD=28\frac{4}{5} \\ KR=CD=\text{?} \end{gathered}

We will solve for the missing side by using the similar triangle theorem. This is shown below:~

\begin{gathered} \Delta MKR\approx\Delta ACD \\ \frac{MK}{AC}=\frac{MR}{AD} \\ \frac{21}{AC}=\frac{24}{28\frac{4}{5}} \\ \text{Cross multiply, we have:} \\ 24\cdot AC=28\frac{4}{5}\cdot21 \\ AC=\frac{28\frac{4}{5}\cdot21}{24}=25\frac{1}{5} \\ AC=25\frac{1}{5} \end{gathered}

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