Question

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

Answer 1

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

`\begin{gathered} \Delta CAB-\Delta CED \\ (CA)/(CE)=(AB)/(ED)=(CB)/(CD) \end{gathered}`
`(AC)/(12)=(7miles)/(21ft)=(CB)/(16ft)`

Please note that

`\begin{gathered} 1mile=5280ft \\ 7miles=7*5280ft=36960ft \end{gathered}`
`\begin{gathered} (AC)/(12)=(36960ft)/(21ft) \\ (AC)/(12)=1760 \\ AC=12*1760ft \\ AC=21120ft \\ AC=(21120ft)/(5280) \\ AC=4miles \end{gathered}`

Hence, AC = 4 miles, OPTION C