Question

City A and B are separated by a 2km wide river and are located as shown in Figure 1 (attached). A road is to be built between city A to B that crosses a bridge straight across the river. Where should the bridge be built (i.e. what is the value of x) so that the road between city A and B is
as short as possible? What is the minimum length of the road?

Answer 1

if someone could help and show working would be greatly appreciated.

Answer 2

@shamim

Answer 3

very interesting question

Answer 4

any luck?

Answer 5

@jeedeee was giving me some ideas , still tossing between them...

Answer 6

what babe

Answer 7

what's the best place for X @jeedeee ?

Answer 8

in the middle

Answer 9

in the middle of what @jeedeee ?

Answer 10

in @mathshelp14 butt

Answer 11

appreciate if it wasn't placed there

Answer 12

why babe x marks the spot for the d

Answer 13

am out of here, this is getting too dirty for my manners

Answer 14

@mathshelp14

Answer 15

the shortest distance is the above hypotenous, cal it H
H = SQRT(17^2 + 14^2) = 22.023 km

Let's find the angle Alpha
tan alpha = 14/17 = 0.8235
alpha = 39.47 degrees

tan alpha = 9 / x
x = 9/tan alpha = 9 / 0.8235 = 10.93 km

Answer 16

the minimum length of the road will be this

A + 2 + B = ?

Answer 17

A = sqrt(9^2 + 10.93^2) = sqrt(200.43) = 14.16 km
B = sqrt(6.07^2 + 3^2) = sqrt(45.85) = 6.77km
I used pythagorean theorem above

now add the 3 to get the shortest road
A+B+2 = 22.93 km

Answer 18

@mathshelp14 are you with me here ? or have I lost you?

Answer 19

thanks for your help but I think it has to do with integration using the distances. Thanks though at least it gives me something to start with.