Question

$\text{Area of a rectangular poster is given as}\frac{24}{9}$ $\text{sq units. What will be the possible length and}$
$\text{breadth of the poster?}$

• A. $\text{Length}=\frac{2}{5}\text{units}$
  $\text{Length}=\frac{1}{3}\text{units}$
• B. $\text{Length}=\frac{6}{3}\text{units}$
  $\text{Length}=\frac{4}{3}\text{units}$
• C. $\text{Length}=\frac{7}{3}\text{units}$
  $\text{Length}=\frac{1}{3}\text{units}$
• D. None of the above

Answer 1

The correct option is B $\text{Length}=\frac{6}{3}\text{units}$

$\text{Length}=\frac{4}{3}\text{units}$
$\text{Area of square wooden piece}=\frac{24}{9}\text{sq. units}$

The denominator here is 9, and the numerator is 24, respectively.

So, the number 2, 3, 4, 6, 8 and 12 has to be the numerator of the side length of the square because
2 × 12 = 24
3 × 8 = 24
4 × 6 = 24

By seeing the options, only 'a' has numerator as 6 and option 'b' has the numerator as 4.

Now, denominators can be 3 only, because:
3 × 3 = 9

So,
Only option 'a' matches both the denominator and the numerator.

$\frac{6}{3}\times \frac{4}{3}=\frac{24}{9}$

So, the correct option is option 'a'.