Question

A grid has lines at 90-degreree angles. There are 12 lines in one direction and 9 lines in the other direction. Lines that are parallel are 11 inches apart. What is the least number of 12in by 12in floor tiles needed to cover all of the line intersections of the grid? The tiles do not have too touch each other.

Answer 1

Answer:

70

Step-by-step explanation:

Given that:

There are twelve (12) lines in a direction and another nine 9 lines in another direction.

If we draw the above illustration out, we will realize that we will have 11 squares by 8 squares.

i.e these 11 squares are 11 inches apart.

Hence, the length of their grid = 11  inches × 11 inches = 121  inches²

Thus, for 12 in by 12 in tiles; we will have:

= $\dfrac {121}{12}$

= $10 \dfrac{1}{12}$

This implies that there are 10 files with just $\dfrac{1}{2}$ inch gap in length.

Similarly, for 8 squares and 11 inches apart;

The width = 8 inches × 11 inches = 88 inches²

Thus; the 12 in tiles needed = $\dfrac{88}{12}$

= $7 \dfrac{1}{3}$

It signifies that there are 7 tiles with $\dfrac{1}{3}$ inch gap in width.

Thus, the least number of tiles required = 10 × 7 = 70