Question

Small rectangular sheets of length units and breadth units are available. These sheets
are assembled and pasted in a big cardboard sheet, edge to edge and made into a square.
The minimum number of such sheets required is​

Answer 1

Answer:

(LCM ( L & B) ) /HCF( L& B)

Step-by-step explanation:

Let say Sides of Rectangular sheets are L & B

Then Smallest possible side of Square would be LCM of L & B

Area of Square = (LCM ( L & B) )²

Area of a rectangular Sheet = LB

Number of Rectangular sheets required = Area of Square / Area of a rectangular Sheet

= (LCM ( L & B) )² / LB

= (LCM ( L & B) ) (LCM ( L & B) ) /LB

as we know that

LCM (L & B)* HCF( L& B) = L * B

=> LCM (L & B) / LB = 1/HCF(L & B)

= (LCM ( L & B) ) /HCF( L& B)

Example

Let say Rectangular sheet size = 4 * 6

then 4 = 2 * 2

& 6 = 2 * 3

LCM = 2 * 2 * 3= 12

HCF = 2

Number of Rectangular Sheets required = 12/2 = 6

Side of square Would be then 4 * 3 = 12 & 2 * 6 = 12