A worker is asked to arrange 1000 identical square tiles into a rectangular pattern and paint only the tiles forming the border. What should be the dimension of the rectangular pattern he arranges, in order to use the minimum amount of paint?

Correct option is D

Solution:

We have 1000 tiles.

Area = length × breadth = 1000

We need to minimize the number of border tiles, i.e., minimize the perimeter or outer boundary.

In general:

For a rectangle, the more "square-like" it is, the smaller the perimeter becomes for the same area.

Thus, dimensions close to a square will require minimum border painting.

Now check given options:

Option (a): 50 × 20

50 × 20 = 1000 (OK)

Not very square-like.

Option (b): 8 × 125

8 × 125 = 1000 (OK)

Very elongated — bad for minimum perimeter.

Option (c): 200 × 5

200 × 5 = 1000 (OK)

Very elongated — even worse.

Option (d): 40 × 25

40 × 25 = 1000 (OK)

40 and 25 are closer — more square-like compared to others.

Thus, 40 × 25 will minimize the paint usage.

Correct answer is (d) 40 tiles × 25 tiles.

Quick Trick:
For a fixed area, square shape minimizes perimeter Always choose dimensions closest to a square.

Information Booster:

For border painting, the more "compact" (less perimeter) the rectangle is, the fewer the tiles to paint.

Elongated rectangles increase boundary tiles.