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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?

116 cm
218 cm
324 cm
4Data inadequate

Answer:- 1

Explanation:-

Solution:

\begin{aligned} \frac{2 (l + b)}{b} = \frac{5}{1} \\ \Rightarrow 2 l + 2 b = 5 b \\ \Rightarrow 3 b = 2 l \\ b = \frac{2}{3} l \\ Then, Area = 216 c m^{2} \\ \Rightarrow l \times b = 216 \\ \Rightarrow l \times \frac{2}{3} l = 216 \\ \Rightarrow l^{2} = 324 \\ l = 18 c m \end{aligned}

$\eqalign{ & \frac{{2\left( {l + b} \right)}}{b} = \frac{5}{1} \cr & \Rightarrow 2l + 2b = 5b \cr & \Rightarrow 3b = 2l \cr & b = \frac{2}{3}l \cr & {\text{Then,}}\,{\text{Area = }}216\,c{m^2} \cr & \Rightarrow l \times b = 216 \cr & \Rightarrow l \times \frac{2}{3}l = 216 \cr & \Rightarrow {l^2} = 324 \cr & l = 18\,cm \cr}$

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", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} \frac{2 (l + b)}{b} = \frac{5}{1} \\ \Rightarrow 2 l + 2 b = 5 b \\ \Rightarrow 3 b = 2 l \\ b = \frac{2}{3} l \\ Then, Area = 216 c m^{2} \\ \Rightarrow l \times b = 216 \\ \Rightarrow l \times \frac{2}{3} l = 216 \\ \Rightarrow l^{2} = 324 \\ l = 18 c m \end{aligned}

$\eqalign{ & \frac{{2\left( {l + b} \right)}}{b} = \frac{5}{1} \cr & \Rightarrow 2l + 2b = 5b \cr & \Rightarrow 3b = 2l \cr & b = \frac{2}{3}l \cr & {\text{Then,}}\,{\text{Area = }}216\,c{m^2} \cr & \Rightarrow l \times b = 216 \cr & \Rightarrow l \times \frac{2}{3}l = 216 \cr & \Rightarrow {l^2} = 324 \cr & l = 18\,cm \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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