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Using the diagram below, what is the length of AC?7 milesB16 ftOA. 7 miOB. 7 ftO C. 4 miDC12 ftE21 ftGiven:1. ACAB-ACED2. AB || ED1 mile = 5280 ft

Using the diagram below what is the length of AC7 milesB16 ftOA 7 miOB 7 ftO C 4 miDC12 ftE21 ftGiven1 ACABACED2 AB ED1 mile 5280 ft class=

Respuesta :

Given: Two similar triangles CAB and CED

To Determine: The value of line AC

Solution

Please note that the ratio of the side lengths of similar triangles are equal. Therefore

[tex]\begin{gathered} \Delta CAB-\Delta CED \\ \frac{CA}{CE}=\frac{AB}{ED}=\frac{CB}{CD} \end{gathered}[/tex][tex]\frac{AC}{12}=\frac{7miles}{21ft}=\frac{CB}{16ft}[/tex]

Please note that

[tex]\begin{gathered} 1mile=5280ft \\ 7miles=7\times5280ft=36960ft \end{gathered}[/tex][tex]\begin{gathered} \frac{AC}{12}=\frac{36960ft}{21ft} \\ \frac{AC}{12}=1760 \\ AC=12\times1760ft \\ AC=21120ft \\ AC=\frac{21120ft}{5280} \\ AC=4miles \end{gathered}[/tex]

Hence, AC = 4 miles, OPTION C

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