Solution 2: Applying the Pythagoras theorem and Guess and Check Since the total distance from the expressway is 6km, we applied different lengths and tried them out using the Pythagoras Theorem until we got the same distance for the road from town A to the expressway and town b to the expressway. The closest distance derived from the start of the expressway which is vertically 2km away from Town A is 3.4km, which makes the other distance from the other end of the expressway to the junction 2.6km

Since Town A is 2km away form the express way, one of the side of the right angle triangle is 2. For Town B, it is 3. Since Town A is nearer to the expressway, the diagonal route towards the junction should be further. Using the Pythagoras theorem, from Town B along the expressway to the junction would be 4km and the diagonal route is 5km. Thus, Town A along the expressway to the junction would be 2km and the diagonal route will be about 3km. So if we increase the distance along the expressway by 1.5km for Town A and decrease the distance along the expressway by 1.5 km for Town B, the diagonal route for Town A to the junction will be about 4km and the diagonal route for Town A to the junction will be about 3.9km. Thus, the junction should be placed 3.5km from town A on the expressway (2.5km away from town B on the expressway).

Solution 2: Applying the Pythagoras theorem and Guess and Check

ReplyDeleteSince the total distance from the expressway is 6km, we applied different lengths and tried them out using the Pythagoras Theorem until we got the same distance for the road from town A to the expressway and town b to the expressway.

The closest distance derived from the start of the expressway which is vertically 2km away from Town A is 3.4km, which makes the other distance from the other end of the expressway to the junction 2.6km

Since Town A is 2km away form the express way, one of the side of the right angle triangle is 2. For Town B, it is 3. Since Town A is nearer to the expressway, the diagonal route towards the junction should be further. Using the Pythagoras theorem, from Town B along the expressway to the junction would be 4km and the diagonal route is 5km. Thus, Town A along the expressway to the junction would be 2km and the diagonal route will be about 3km. So if we increase the distance along the expressway by 1.5km for Town A and decrease the distance along the expressway by 1.5 km for Town B, the diagonal route for Town A to the junction will be about 4km and the diagonal route for Town A to the junction will be about 3.9km. Thus, the junction should be placed 3.5km from town A on the expressway (2.5km away from town B on the expressway).

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