Hustrative Mathematics
Lesson 1: A Different kind of Change
Cool Down: 100 Meters of Fencing
A rectangular yard is enclosed by 100 meters of fencing. The table shows some possible
values for the length and width of the yard.
length (meters) width (meters) area (square meters)
10
40
400
20
30
25
25
625
35
15
525
40
1. Complete the table with the missing values.
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Aking and his army will attempt to capture a fortress. the left and right flanks break off from the main group to attack the west and east guard towers. suppose the left flank has a 60% chance of success and the right flank has a 75% chance of success, independently of one another. if both flanks capture their respective targets, then the king has a 98% chance of successfully taking the fort. if, however, only the left flank captures its tower, the king has an 80% chance of success; if only the right flank succeeds, the king has a 50% chance. if both flanks fail, then the king's chance of capturing the fort drops to 20%. it turns out the king captures the fort. what is the probability that one, and only one, flank was successful (either the left, or the right, but not both)? (round your answer to 3 decimal places)