306 Answersthe pencil is at F the length of string is 12 + (12 - 2x) = 24 - 2x, and
when the pencil is at C the length of string is 2(12 - x) = 24 - 2x also,
proving the correctness of the solution.
- THE BRICKLAYER'S TASK
A glance at the illustration will show that if you could cut off the portion
of wall marked 1 and place it in the position indicated by 2, you would have
.-----~1Z~~~; __ .·.·~
A B Ca piece of straight wall, BC, enclosed by the dotted lines, exactly similar to the
wall AB. Therefore, both men were wrong, and the price should be the same
for the portion of wall that went over the hill as for the part on the level. Of
course, the reader will see at a glance that this will only apply within a certain
limitation. But an actual drawing of the wall was given.306. MEASURING THE RIVER
Measure any convenient distance
along the bank from A to C, say 40
yards. Then measure any distance
perpendicularly to D, say 12 yards.
Now sight along DB and find the
point E. You can then measure the
distance from A to E, which will here
be 24 yards, and from E to C, which
will be 16 yards. Now AB: DC =
AE: EC, from which it is evident that
AB, the width of the river, must be
18 yards.