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The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
Options:
A .  16 cm
B .  18 cm
C .  14 cm
D .  20 cm
Answer: Option B

Answer : Option B

Explanation :

$MF#%\text{Given that }\dfrac{2(l + b)}{b} = 5$MF#%


=> 2l + 2b = 5b
=> 2l = 3b

$MF#%=> b = \dfrac{2l}{3}$MF#%


Also given that area = 216 cm2
=> lb = 216 cm2

$MF#%\begin{align}
&\text{Substituting the value of b, we get, }l \times \dfrac{2l}{3} = 216\\\\
&\Rightarrow l^2 = \dfrac{3 \times 216}{2} = 3 \times 108 = (3 \times 3) \times 36\\\\
&\Rightarrow l = 3 \times 6 = 18\text{ cm}
\end{align} $MF#%



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