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?<…

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asked Sep 17, 2023 225k views

1 Answer

Cgons · Answer 1 · 2023-09-22T23:43:57+0000

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

$\bar{AD}=500-320=180$

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

$\begin{gathered} (BD)/(CD)=(CD)/(AD) \\ (320)/(x)=(x)/(180) \end{gathered}$

Let us solve for x

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

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