Two pillars are placed vertically 8 feet apart. The height difference of the two pillars is 6 feet. The two ends of a rope of length 15 feet are tied to the tips of the two pillars. The portion of the length of the taller pillar that can be brought in contact with the rope without detaching the rope from the pillars is

The correct answer is Option 2. To find the maximum length of the taller pillar that the rope can touch, we must pull the rope taut towards the base of the taller pillar while it remains attached to the tip of the shorter pillar.

Let the shorter pillar have height h and the taller h + 6. The rope (length 15) is fixed at the tip of the shorter pillar. To touch the taller pillar at a point x feet below its tip, we form a right-angled triangle where:

• The horizontal distance (base) is 8 feet.
• The vertical distance from the shorter tip to the contact point is |6 - x|.
• The rope length required is the hypotenuse, which must be 15 feet.

Applying Pythagoras' theorem: 8² + (6 + x)² = 15². This gives (6 + x)² = 225 - 64 = 161. Thus, 6 + x = √161 (approx. 12.68). Solving for x, we get 6.68 feet. This value is clearly more than 6 feet but less than 7 feet.