Sajjad1994 wrote:
The straight-line distance between Town A and Town B is 15 km. Most travelers passing through the towns, however, use two highways-first traveling × km west from Town A on one highway and then traveling y km north to Town B on a different highway. The intersection of these highways is farther from Town A than Town B.
Select values for x and for y that are jointly consistent with the given information. Make only two selections, one in each column.
The highway is East to West and then South to North. => Thus, intersection of two highways is 90 degree.
A to B is 15 => The hypotenuse is 15.
Solution is that we have to find the pair whose square adds up to \(15^2\).
Remember, a very commonly used triplet is 3:4:5 and here we have 5x as 15 or x=3
Thus, the sides are 3*3:3*4:3*5 or 9:12:15
Longer side is Town A, so 12.
A=>12
B=>9
Choice E has to be 12.
Just adding more data and getting this post in the beggining to substantiate why I feel 13 as an answer would open a pandora box.We could justify 13 as an answer only by one logic and that would be: The highways may not be at 90 degree, then a slight sharp angle of 83 degree would give the distances as 9-13-15.
But a slightly more sharper angle of around 80 degree would give distances as 10-13-15, or a more wider angle of around of 104 degree would justify distances 9-10-13.Almost all values will get justified as 15 will have to be less than the sum of other two sides and more than the difference of the other two sides.