Question

two poles, one 12 meters tall and one 30 meters tall, stand 40 meters apart. a worker attaches a piece of wire to the top of each pole and anchors the other ends of these wires to a stake in the groundsomewhere between the two poles. how far from the 12-meter pole should the worker position the stake to use the least amount of wire?

Answer 1

To minimize the amount of wire used, the worker should position the stake approximately 26.67 meters from the base of the 12-meter pole.

Step-by-step explanation:

To find the position of the stake that minimizes the amount of wire used, we can use the concept of similar triangles. The ratio of the height of the shorter pole (12 meters) to the distance of the stake from the base of the shorter pole is equal to the ratio of the height of the taller pole (30 meters) to the distance of the stake from the base of the taller pole. Let's call the distance of the stake from the base of the shorter pole x. Using this information, we can set up the following equation:

(x + 40) / x = 30 / 12

Cross-multiplying and solving for x, we get:

12x + 480 = 30x

480 = 18x

x = 26.67 meters

Therefore, the worker should position the stake approximately 26.67 meters from the base of the 12-meter pole to use the least amount of wire.