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help me solve pleaseMarla walks straight from the parking lot to the lake as shown, where the sign reads that she is 320 m from the dock. How far is Marla from the parking lot?

help me solve pleaseMarla walks straight from the parking lot to the lake as shown, where the sign reads that she is 320 m from the dock. How far is Marla from class=

Answer :

As you can see in the given figure,

The parking lot is at point C and Maria is at point D

We are asked to find the length CD (marked x)

As you can see there are two triangles.

Triangle △ADC and △BDC

The length of side AD is given by

[tex]\bar{AD}=500-320=180[/tex]

Now we can apply the property of similar triangles, if the triangles are similar then the ratio of corresponding sides will be equal

[tex]\begin{gathered} \frac{BD}{CD}=\frac{CD}{AD} \\ \frac{320}{x}=\frac{x}{180} \end{gathered}[/tex]

Let us solve for x

[tex]\begin{gathered} \frac{320}{x}=\frac{x}{180} \\ x\cdot x=320\cdot180 \\ x^2=57600 \\ x=\sqrt[]{57600} \\ x=240\: m \end{gathered}[/tex]

Therefore, Maria is 240 m away from the parking lot.

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