Question

The length of a rectangular hall is $\frac{4}{3}$ of its width. If the area of the hall is $300$m${}^2$ ,what is the difference between the length and breadth ?

• A. $15$ m
• B. $20$ m
• C. $3$ m
• D. $5$m

Answer 1

Answer: (D)

$5$m

Let the width of rectangular hall be $xm$

So, the length of the rectangular hall $=(\frac{4}{3}\times x)m$

$\Rightarrow$ Area $=(l\times b)m^3$

$=(x^2\times \frac{4}{3})m^3$

$\Rightarrow$ Area ( given ) $=300m^3$

$\therefore x^2\times \frac{4}{3}=300$

$x^2=\frac{900}{4}$

$x^2=225$

$x=15m$

$\therefore$ width $=15m$

length $=(\frac{4}{3}\times 15)m=20m$

$\therefore$ Difference $=(length-width)=20m-15m=5m$

Hence, the answer is $5m.$