Question

a Courtyard is in the shape of a rectangle of length 11.2 m and breadth 7.2 m find the measure of the side of the largest square shaped tile that can be used to cover the Courtyard completely . how many such tiles are needed for the purpose?​

Answer 1

Given :

The Length of the rectangular courtyard = L = 11.2 m

The breadth of rectangular courtyard = B = 7.2 m

To Find :

The measure of the side of the largest square shaped tile that can be used to cover the Courtyard completely

Solution :

Area of rectangle = Length × Breadth

Or,  Area of rectangle = L  × B

Or,  Area of rectangle = 11.2 m  × 7.2 m

∴   Area of rectangle = 80.64 sq m

∵  square shaped tile that can be used to cover the Courtyard completely

Let The measure of each side of square tiles = x m

Length = 11.2 m = 1120 cm

Breadth = 7.2 m = 720 cm

So, square shaped tile that can be used to cover the Courtyard completely = HCF of 1120 cm , 720 cm

i.e   factor of 1120 = 2 × 2 × 2 × 2 × 2 × 5 × 7

      factor of 720 = 2 × 2 × 2 × 2 × 3 × 3 × 5

So, HCF of 1120 and 720 =  2 × 2 × 2 × 2 × 5 = 80

So, The largest size of square tiles  that can be used to cover the Courtyard completely = x = 80 cm

Again

Area of square tiles = side × side

∴ Area of square tiles = 80 cm × 80 cm

i.e Area of square tiles = 6400 sq cm  = 0.64 sq m

Now,

Number of square tile = $\dfrac{Area of rectangular courtyard}{Area of square tiles}$

Or,         N = $\dfrac{80.64}{0.64}$

∴ Number of tiles = N = 126

Hence,  The largest size of square tiles  that can be used to cover the Courtyard completely is 80 cm

And The number of tiles needed to  to cover the Courtyard completely is 126  . Answer