Question

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The sides of a rectangular park are in the ratio 4 : 3. If its perimeter is 392 m, find

its length and breadth​.
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Answer 1

Answer:

The sides of a rectangular park are in the ratio 4 : 3. If its perimeter is 392 m, find its length and breadth

\begin{gathered} \\ \\ \end{gathered}

Given :-

Length and Breadth of the Rectangle are in the ratio = 4:3

Perimeter of the Rectangle = 392m

\begin{gathered} \\ \\ \end{gathered}

To Find :-

Measures of Length and Breadth of Rectangle .

\begin{gathered} \\ \\ \end{gathered}

Solution :-

\begin{gathered} \\ \end{gathered}

Let the Length be 4x

Let the Breadth be 3x

\begin{gathered} \\ \end{gathered}

According To Question :-

\begin{gathered}\qquad \quad {:} \longrightarrow \sf\boxed{\bf{Perimeter \: = \: 2(Length \: + \: Breadth) }}\\\end{gathered}

:⟶

Perimeter=2(Length+Breadth)

\begin{gathered}\qquad \quad {:} \longrightarrow \sf{\sf{392 \: = \: 2(\: 4x \: + \: 3x) }}\\\end{gathered}

:⟶392=2(4x+3x)

\begin{gathered}\qquad \quad {:} \longrightarrow \sf{\sf{392 \: = \: 2\: \times \: 7x }}\\\end{gathered}

:⟶392=2×7x

\begin{gathered}\qquad \quad {:} \longrightarrow \sf{\sf{392 \: = \: 14x }}\\\end{gathered}

:⟶392=14x

\begin{gathered}\qquad \quad {:} \longrightarrow \sf{\sf{\cancel\dfrac{392}{14} \: = \: x }}\\\end{gathered}

:⟶

14

392

=x

\begin{gathered}\qquad \quad {:} \longrightarrow \sf{\bf{28 \: = \: x }}\\\end{gathered}

:⟶28=x

━━━━━━━━━━━━━━━━━━━━━━━━━

Length = 4x = 4 × 28 = 112m

Breadth = 3x = 3 × 28 = 84m

━━━━━━━━━━━━━━━━━━━━━━━━━

\begin{gathered}\begin{gathered}\begin{gathered}\qquad \therefore\: \sf{ Length \: = \underline {\underline{ 112m}}}\\\end{gathered}\end{gathered} \end{gathered}

∴Length=

112m

\begin{gathered}\begin{gathered}\begin{gathered}\qquad \therefore\: \sf{ Breadth \: = \underline {\underline{ 84m}}}\\\end{gathered}\end{gathered} \end{gathered}

∴Breadth=

84m