Question

4. The length of a floor is 4 m 44 cm and
the breadth is 3 m 30 cm. What is the
maximum length of square tiles that can
completely cover the floor?​

Answer 1

Solution:

Length of floor = 4 m 44 cm = [ (4 * 100) + 44 ] cm = 444 cm

Breadth of floor = 3 m 30 cm = [ (3 * 100) + 30 ] cm = 330 cm

GCD(Greatest Common Divisor) means to take out the highest common divisor of two positive integers.

Now, we will take Greatest Common Divisor of both numbers,

444 = 2 * 2 * 3 * 37

330 = 2 * 3 * 5 * 11

GCD of 444 and 330 = 2 * 3 = 6

We took those factors which were common in both and multiplied.

Maximum Length of the square tile =>

Greatest number which divides both length and breadth of floor i.e. GCD of 444 and 330

Maximum Length of the square tile => 6 cm

The maximum length of square tiles that can  completely cover the floor is 6 cm.

Answer 2

$\underline{\underline{\bf{\bigstar \: Figure : }}}$

$\:\:$

$\setlength{\unitlength}{1.6mm}\begin{picture}(5,6)\put(0,25){\line(1,0){35}}\put(0,0){\line(1,0){35}}\put(0,0){\line(0,1){25}}\put(35,0){\line(0,1){25}}\put(17,-2){4m 44cm}\put(18,-2){}\put(35,15){3m 30cm}\put(18,0){ }\end{picture}$

$\:\:$

$\underline{\underline{\bf{\bigstar \: Solution : }}}$

$\:\:$

$\footnotesize{\red{ Length\: of\: floor = 4m\,44cm }}$

$\footnotesize{\red{\implies Length\: of\: floor = 444cm }}$

$\:\:$

$\rule{200}3$

$\:\:$

$\footnotesize{\blue{ Breadth\: of\: floor = 3m\:30cm }}$

$\footnotesize{\blue{\implies Breadth\: of\: floor = 330cm }}$

$\:\:$

$\rule{200}3$

$\:\:$

$\footnotesize{\green{ Side\: of\: tiles = HCF \:of\: Length \: and\: breadth }}$

$\footnotesize{\green{\implies Side\: of\: tiles = HCF \:of\:444cm \: and\:330cm }}$

$\footnotesize{\green{\implies Side\: of\: tiles = 6cm }}$

$\:\:$

$\bold{\pink{ Side\: of\: tiles \: is\: 6cm }}$