+8 Derek plans to hang a shelf in his attic. The walls are sloped and meet at the peak point A, as shown in the figure below where wall AB is 7 feet long and wall AC is 9 feet long. A hole for shelf DE is drilled on wall AB 4 feet up the wall so that BD = 4. Since Derek wants the shelf to be parallel to floor BC, where should he drill hole E?
+36916 Not sure I can visualize this,,,,,but if the first hole is drilled 4 feet up from the bottom of the first wall....that is 3 feet down from the top....drill the other hole 3 feet down from the top on the other wall (or 6 feet up from the botom)....I think.
+128475 We have something like this :
A
3
D E
4
B C
Since DE is parallel to BC, by Euclid........AD/DB = AE/ EC
And AE = 9 - EC .....so we have.....
3 / 4 = [9 - EC] / EC cross-multiply
3EC = 4 [9 - EC]
3EC = 36 - 4EC
7EC = 36 divide both sides by 7
EC = 36/7 = about 5.14 ft ....So E should be about 5.14 ft from C on AC
Proof :
Note = AE = 9 - EC = 9 - 36/7 = 27/7
So
AD/DB = AE/EC
3/4 = [27/7] / [36/7]
3/4 = 27/26
3/4 = 3/4
