Question

.If the perimeter and length of a rectangle is 6:1 and the area of the rectangle is 288 cm^2 . Then find the length​

Answer 1

Answer:

OK ----___----XD

Step-by-step explanation:

Let the length be 2x and breadth be x

then,

Area, 2x

2

=288

⇒x

2

=144

⇒x=12

∴2x=24

Hence length=24,breadth=12

∴Perimeter =2(12+24)=72cm

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OK _-----____-------__------_--XD

Answer 2

$\maltese\LARGE\textsf{\underline{ FiGuRe :-}}$

$\large\textsf{ }$

$\large\textsf{Length = 12cm}$

$\boxed{\begin{array}{ c c c c } \; \; \; \; & \; \; \; \; & \; \; \; \; & \; \; \; \; \\\\ \; \; \; \; & \; \; \; \; & \; \; \; \; & \; \; \; \; \\\\ \; \; \; \; & \; \; \; \; & \; \; \; \; & \; \; \; \;\end{array}}$ Breadth = 24cm

$\large\textsf{ }$

$\maltese\LARGE\textsf{\underline{ SoLuTioN :-}}$

$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\large\textsf{Ratio of Perimeter to length = 6 : 1}$

$\large\textsf{ }$

↦ Let's assume x as the common multiple :-

$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\large\textsf{Perimeter = 6x}$

$\qquad\tt{:}\longrightarrow\large\textsf{Length = x}$

$\large\textsf{ }$

↦ We know that :-

$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\boxed{\large\textsf\textcolor{purple}{ {\large\textsf{Area}}_{\large\textsf{( \; Rectangle \; )}} = \large\textsf{ length × breadth} }}\\\\\\\qquad\tt{:}\longrightarrow\boxed{\large\textsf\textcolor{purple}{ {\large\textsf{Perimeter}}_{\large\textsf{( \; Rectangle \; )}} = \large\textsf{2 ( l + b )} }}$

$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\large\textsf{2 ( l + b ) = Perimeter}$

$\qquad\tt{:}\longrightarrow\large\textsf{2 ( x + b ) = 6x}$

$\qquad\tt{:}\longrightarrow\large\textsf{2x + 2b = 6x}$

$\qquad\tt{:}\longrightarrow\large\textsf{2b = 6x - 2x}$

$\qquad\tt{:}\longrightarrow\large\textsf{ b = \cfrac{\large\textsf{4x}}{\large\textsf{2}} }$

$\qquad\tt{:}\longrightarrow\large\textsf{b = 2x ----- ( i )}$

$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\large\textsf{length × breadth = Area}$

$\qquad\tt{:}\longrightarrow\large\textsf{x × 2x = 288 ----- [ From ( i ) ]}$

$\qquad\tt{:}\longrightarrow\large\textsf{2x² = 288}$

$\qquad\tt{:}\longrightarrow\large\textsf{ x²= \xcancel{\cfrac{\large\textsf{288}}{\large\textsf{2}}} }$

$\qquad\tt{:}\longrightarrow\large\sf{x = √144}$

$\qquad\tt{:}\longrightarrow\boxed{\large\textsf{∴ x = 12}}$

$\large\textsf{ }$

$\large\texttt\textcolor{orange}{∴ Length = 12cm}$