Question

Length of a board is $12$ feet and width is $11$ feet. How many boards of same area can be manufactured given that length and breadth of the board should have integer values and length is less than breadth..

• A. $5$
• B. $6$
• C. $7$
• D. $8$

Answer 1

The correct option is B $6$

Length of floor $=12$ feet
Width of floor $=11$ feet
Area of floor $=length\times width$
$=11\times 12=132$ $fee{t}^2$

$132$ is a composite number having factors other than $1$ and itself.

Factors of 132 are
$132=1\times 132132=2\times 66132=3\times 44132=4\times 33132=6\times 22132=11\times 12$

Hence, 6 boards can be manufactured.