Question:
The length of a rectangular field is three times its breadth. If the area of the field by 147 sq metres, find the length of the field.
Solution:
Let the length and breadth of the rectangle be $3 x \mathrm{~m}$ and $x \mathrm{~m}$, respectively.
According to the question:
$3 x \times x=147$
$\Rightarrow 3 x^{2}=147$
$\Rightarrow x^{2}=49$
$\Rightarrow x=7$ or $x=-7$
$\Rightarrow x=7 \quad(\because x$ cannot be negative $)$
$\therefore$ Length $=3 \times 7=21 \mathrm{~m}$
Breadth $=7 \mathrm{~m}$