Question

How many square pieces as large as possible of identical dimensions can be cut from a rectangular field of 200 m long and 80 m wide?

Answer 1

Hello Dear.

Given ⇒

Length of the Rectangular Field = 200 m.
Breadth of the Rectangular Field = 80 m.

∵ Area of the Rectangular Field = Length × Breadth
∴ Area  = 200 × 80
∴ Area = 16000 m².


According to the Question, Square pieces must be as large as Possible.
So, Taking the Side of the Square be 50 m.

∴ Area of 1 Square Pieces = 50 × 50
   = 2500 m²

No. of pieces = 16000/2500
= 6.4
Since, number of pieces can not in decimals, therefore Rejecting side = 50 cm and taking the new dimensions.

If Side of the Square pieces = 80 m.
Then, Area = 3600 m²
∴ No. of pieces = 16000/3600
   = 4.44
Thus, It cannot be possible.


Now, Taking the Side of the Square be 40 m.
Then Area = 40 × 40
   = 1600 m²

∵ No. of pieces = Total Area of the Field/Area of the 1 Square pieces.
   = 16000/1600
   = 10 pieces.


Hence, 10 Square pieces of side 40 m each can be cut from the rectangular field of 16000 m².


Hope it helps.

Answer 2

Answer: find hcf of 200 and 80

                        200 = 2 x 2 x 2 x 5 x 5

                        80    = 2 x 2 x 2 x  5 x 2

                                    =2 x 2 x 2 x 5

                                    = 40 / 4

                                      = 10

Explanation:the sides of square =4

                                    gcd of 200 and 80 =40

                                                                     = 40 divide by 4  

                                                                      =10

                                so answer is 10