Question

a rectangular courtyard is 18m 72cm long and 13m 20cm broad. it is to be paved with squared tiles in the same size .find the least possible no. of such tiles ​

Answer 1

GIVEN :-

• Length of rectangular courtyard = 18m 72 cm

                                                              = 1800 + 72 cm

                                                              = 1872 cm

• Breadth of rectangular courtyard = 13m 20cm

                                                                = 1300 + 20 cm

                                                                = 1320 cm

• Rectangular courtyard is to paved with squared tiles in the same size.

TO FIND :-

• The least possible number of such tiles.

SOLUTION :-

  According to the question,

  Length of side of square tile = HCF of length and breadth of the

                                                        rectangular courtyard

   Prime factorization of 1872 = 2 × 2 × 2 × 2 × 3 × 3 × 3

   Prime factorization of 1320 = 2 × 2 × 2 × 3 × 5 × 11

   HCF of 1872 and 1320 = 2 × 2 × 2 × 3

                                         = 24

   ∴ Length of side of square tile = 24 cm

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

                               = $\sf \dfrac{1872 \times 1320 }{24 \times 24 }$

                                = $\sd\dfrac{2471040}{576}$

                                = $\bf 4290$

     

Least  possible number of tiles = 4290 tiles