Question

Habib wants to cover a kitchen wall in ceramic tile. The wall is 42 feet by 10 feet.
What is the side measure of the largest square tile that he can use to cover the whole wall so there is no overlap or cutting?

Answer 1

Answer: Side of largest square tile will be 105 feet.

Explanation:

Since we have given that

dimensions of the wall is 42 feet by 10 feet

So,

Length of wall = 42 feet

Breadth of wall = 10 feet

First we calculate the H.C.F. of 42 and 10,

which is 2 only.

The largest square tile side would be 2 feet.

Now, we find the number of tiles used,

Number of tiles =

$\frac{\text{Area of wall}}{\text{H.C.F. of }42\text{ and }11\times\text{ H.C.F. of }42\text{ and } 11}}\\\\=\frac{42\times 10}{2\times 2}\\\\=\frac{420}{4}\\\\=105$

We get integer value of number of tiles.

Therefore, Side of largest square tile will be 2 feet.