Question

find the length and breadth of the rectangle if the peremetre is 72 length is 5x+4 and breadth is x-4​

Answer 1

$\LARGE\textbf{\underline{\underline{Given :-}}}$

$\qquad\tt{:}\longrightarrow\large\textsf{Length of the rectangle = 5x + 4 }$

$\qquad\tt{:}\longrightarrow\large\textsf{Breadth of the rectangle = x - 4 }$

$\qquad\tt{:}\longrightarrow\large\textsf{Perimeter of the rectangle = 72 unit's }$

$\LARGE\textbf{\underline{\underline{To \; Find :-}}}$

$\qquad\tt{:}\longrightarrow\large\textsf{Length and Breadth of the rectangle = ? }$

$\LARGE\textbf{\underline{\underline{Formula :-}}}$

$\bigstar\boxed{\large\textsf{ {\large\textsf\textcolor{red}{Perimeter}}_{\large\textsf\textcolor{red}{( \; Rectangle \; )}} \large\textsf\textcolor{red}{ = 2 ( l + b )} }}$

$\LARGE\textbf{\underline{\underline{Solution :-}}}$

• Inserting the given values in the Formula of the perimeter of the rectangle .

• Length ( l ) = 5x + 4
• Breadth ( b ) = x - 4
• Perimeter = 72 unit's

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$\large\textsf\textcolor{orange}{ {\large\textsf\textcolor{orange}{Perimeter}}_{\large\textsf{( \; Rectangle \; )}} \large\textsf\textcolor{orange}{= 2 ( l + b )} }\\\\\\\qquad\tt{:}\longrightarrow\large\textsf{ \; \; 72 = 2[( 5x + 4 ) + ( x - 4 )] }\\\\\\\qquad\tt{:}\longrightarrow\large\textsf{ \; \; 72 = 2( 5x + 4 + x - 4 )}\\\\\\\qquad\tt{:}\longrightarrow\large\textsf{\; \; 72 = 2( 5x + x + 4 - 4 )}\\\\\\\qquad\tt{:}\longrightarrow\large\textsf{\; \; 72 = 2 × 6x }\\\\\\\qquad\tt{:}\longrightarrow\large\textsf{\; \; 72 = 12x}\\\\\\\qquad\tt{:}\longrightarrow\large\textsf{ \; \; 12x = 72 }\\\\\\\large\textsf{ x = \cfrac{\large\textsf{72}}{\large\textsf{12}} }\\\\\\\qquad\tt{:}\longrightarrow\boxed{\underline{\large\textsf\textcolor{purple}{\; \; x = 6 }}}$

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$\qquad\tt{:}\longrightarrow \large\textsf{Length = 5 × 6 + 4}\\\\\qquad\tt{:}\longrightarrow\large\textsf{\; \; \; = 30 + 4}\\\\\qquad\tt{:}\longrightarrow \large\textsf\textcolor{green}{ \; \; \; = 34 units}$

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$\qquad\tt{:}\longrightarrow\large\textsf{Breadth = 6 - 4 }\\\\\qquad\tt{:}\longrightarrow\large\textsf\textcolor{green}{ \; \; \; = 2 units}$

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Answer 2

Answer:

Length = 34 units

Breadth = 2 units

Step-by-step explanation:

Perimeter of rectangle = 2(L + B)

Here,

Perimeter = 72

L = 5x + 4

B = x - 4

Therefore,

=> 2(5x + 4 + x - 4) = 72

=> 2(6x) = 72

=> 12x = 72

=> x = 72/12

=> x = 6

So,

L = 5x + 4 = 5(6) + 4 = 30 + 4 = 34 units

B = x - 4 = 6 - 4 = 2 units