On one straight line at an equal distance from each other on one side of the road there are three telegraph poles. The outermost ones are at distances of 1.5 m and 7.5 m from the road. Find the distance at which the middle post is from the road.
1. The location of the pillars relative to the road is a geometric figure in the form of a trapezoid.
2. Let us denote the vertices of this trapezoid by symbols A, B, C, D.
3. The length of the side of the trapezoid AD (one of the bases) is 1.5 meters. The length of the BC side (second base) is 7.5 meters.
The bases of AD and BC are parallel.
4. KM – perpendicular to AB (distance from the middle pillar to the road).
5. Since the distances between the posts are the same, the KM is the middle line of the trapezoid.
KM = (BC + AD) / 2 = (7.5 + 1.5) / 2 = 4.5 meters.
Answer: The middle post is 4.5 meters from the road.
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