As shown in the figure, the distance between a and B on the railway is 25km, C and D are two villages, Da ⊥ AB is in a, CB ⊥ AB is in B, known Da = 15km, CB = 10km, now we need to build a local product acquisition station E on the railway AB, so that the distance between C and D villages and E station is equal, then how many kilometers should e station be built from a station?

As shown in the figure, the distance between a and B on the railway is 25km, C and D are two villages, Da ⊥ AB is in a, CB ⊥ AB is in B, known Da = 15km, CB = 10km, now we need to build a local product acquisition station E on the railway AB, so that the distance between C and D villages and E station is equal, then how many kilometers should e station be built from a station?

Let AE = XKM, ∵ C and D villages have the same distance to e station, ∵ de = CE, that is, de2 = CE2. According to Pythagorean theorem, we can get 152 + x2 = 102 + (25-x) 2, x = 10. Therefore, e point should be built 10km away from a station

As shown in the figure, a and B on the railway are 25km apart, C and D are two villages, Da is perpendicular to a, AB is perpendicular to B, Da = 15km, CB = 10km. Now we need to build a local specialty purchasing station E on the railway AB, so that the distance between C and D villages and E station is equal, so how many kilometers should e station be built from a point?

As shown in the figure, the distance between villages ∵ C and D and station e is the same, ∵ CE = de in RT △ DAE and RT △ CBE, de = AD + AE, CE = be + BC ∵ AD + AE = be + BC, if AE is x, then be = 25-x, BC = 10 and Da = 15 are substituted into the formula of X + 15 = (25-x) + 10. After sorting out, 50x = 500, the solution is x = 10, ∵ e station should be built in the distance from a