Question

from a cardboard of 42cm length and 30 cm breadth squares of the same size are to be cut. find the least possible number of squares​

Answer 1

Given:

The dimensions of the rectangular cardboard:

length = 42 cm

breadth = 30 cm

Square of the same size are to be cut

To find:

The least possible number of squares​

Solution:

Firstly we have to find the maximum possible size of the square that is to be cut from the rectangular cardboard.

For this, we will find the H.C.F. of the given length and breadth i.e., H.C.F. of 42 cm and 30 cm.

Therefore,

42 = 2 × 3 × 5

30 = 2 × 3 × 7

∴ H.C.F. = 2 × 3 = 6 ← maximum possible size of the square i.e., side of the square = 6 cm

Now,

The required no. of squares is given by,

= $\frac{Area \: of\:rectangular\:cardboard}{Area \:of\:each\:square}$

= $\frac{Length\:\times\:Breadth}{[Side]^2}$

substituting the values

= $\frac{42\:\times\: 30 }{[6]^2}$

= $\frac{1260 }{36}$

= $\bold{35}$

Thus, the least possible no. of squares is 35.

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