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19 Apr 2023, 10:16
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
100% (02:42) correct
0%
(00:00)
wrong
based on 5
sessions
History
Date
Time
Result
Not Attempted Yet
John, a courier delivery agent, starts at point A and makes a delivery each at points B, C and D, in that order. He travels in a straight line between any two consecutive points. The following are known: (i) AB and CD intersect at a right angle at E, and (ii) BC, CE and ED are respectively 1.3 km, 0.5 km and 2.5 km long. If AD is parallel to BC, then what is the total distance (in km) that John covers in travelling from A to D?
A. 10.5
B. 12.5
C. 11.5
D. 15.5
E. 18.5
adapted from CL
A. 10.5
B. 12.5
C. 11.5
D. 15.5
E. 18.5
adapted from CL
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19 Apr 2023, 23:50
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rd1009
We can visualize the information as shown below -
Attachment:
Screenshot 2023-04-20 120140.jpg
In \(\triangle CEB\)
\(\angle BEC = 90\), therefore
\(CB^2 = CE^2 + BE^2\)
\(BE^2 = (\frac{13}{10})^2 - (\frac{5}{10})^2\)
\(BE^2 = \frac{144}{100}\)
\(BE = \frac{12}{10}\)
\(\triangle EDA\) \( \approx\) \(\triangle ECB\)
Therefore
\(\frac{ED}{EC} = \frac{EA}{EB}\)
\(\frac{2.5}{0.5} = \frac{EA}{1.2}\)
EA = \(\frac{60}{10}\) = 6
Total Distance = AE + EB + BC + CE + ED = 6 + 1.2 + 1.3 + 0.5 + 2.5 = 11.5
Option C
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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