Question

$ 50 $ square stones slabs of equal size were needed to cover a floor area of $ 72\,sq.\,m $ . The length of each stone slab is
 $
  (A)\,102\,cm \\
  (B)\,120\,cm \\
  (C)\,201\,cm \\
  (D)\,210\,cm \\
 $

Answer 1

Hint: In this we first let the side of the square slab as x, then using it we find an area of $ 50 $ slabs and equate the area so obtained to the area of floor to get the value of ‘x’. As it is given that $ 50 $ slabs cover the whole area of floor.

Complete step-by-step answer:
Let the length of each stone slab is x
Since, it is given that the stone slab is in square shape.
Therefore area of one stone slab is = $ {x^2} $
Also, there are $ 50 $ such slabs.
Hence, area because of $ 50 $ slabs given as = $ 50{x^2} $
Also, it is given that $ 50 $ slabs are needed to cover the complete floor.
Therefore, the area of $ 50 $ slabs will be equal to the area of the floor.
The total area of the floor is $ 72\,sq.\,m $
Hence, from above we see that the area of $ 50 $ slab will be equal to the area of the floor.
 $
   \Rightarrow 50{x^2} = 72 \\
   \Rightarrow {x^2} = \dfrac{{72}}{{50}} \\
   \Rightarrow {x^2} = 1.44 \\
   \Rightarrow x = 1.2 \\
 $
Therefore, from above we see that length of each slab is $ 1.2m $ or $ 120\,cm $
Hence, from given four options we see that option (B) is the correct option.

Note: : In mensuration we see that if we divide any big area in smaller regions of fixed shape. Then the sum of the area of smaller regions will always equal the area of the big region whose parts have been done.