Rajesh, 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 Rajesh covers in travelling from A to D?
Solution
Based on the information, the following figure can be obtained.
Given, CE=0.5, BC = 1.3 and ED=2.5
Triangle CEB is a right-angled triangle => EB = 1.2
$$\triangle\ $$ ECB is similar to $$\triangle\ $$ EDA
EB/EC = AE/ED => AE = 6
Hence total distance travelled = AB + BC + CD = 7.2 + 1.3 + 3 = 11.5km
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