Question

Find the largest size of square tile that can be used for paving a rectangular plot 90 m by 171m. Find also the number of tiles that will be needed.

Answer 1

The largest size of square tile used for paving is 9m.

The number of tiles used is 1,710.

Given,

The length of the rectangular plot = 171 m

The breadth of the rectangular plot = 90m

To Find,

The largest size of a square tile.

The number of tiles Used.

Solution,

Firstly, we will find the area of the rectangle,

using the formula of Area.

Area = Length × Breadth

where,

Length = 171m

Breadth = 90m

Area of rectangle = 171 × 90

Area of rectangle = 15,390m

Now, we will find the factors of 171m and 90m,

90 = 3 × 3 × 10.

171 = 3 × 3 × 19.

The HCF of 90 and 171 is

= 3 × 3

= 9m

The size of the largest tile is 9m.

So,

the number of square tiles that can be used for paving a rectangular plot = Area of rectangle / Size of one tile

= 15390/9

On dividing, we get,

= 1,710.

The largest size of square tile used for paving is 9m.

The number of tiles used is 1,710.

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