Question

The length of a rectangle is twice is breadth and is perimeter 180 find the diamensions

Answer 1

Given :-  

• The length of a rectangle is twice is breadth  

• Perimeter of rectangle is 180  

To Find :-  

• Dimensions of the rectangle  

Solution :-  

~Here , in this question we’re given that the length is twice the breadth and value of the perimeter and we need to find the length and breadth of the rectangle . We can find them by putting the values in the formula of finding perimeter of a rectangle .  

_____________

Let the breadth be ‘ x ‘  

Then length will be ‘ 2x ‘  

_____________

⊕ As we know that ,  

Perimeter = 2 ( l + b )  

Where ,  

• L is the length  
• B is the breadth  

_____________

Let’s solve by putting the values !

$\sf \implies 180 = 2 ( x + 2x )$

$\sf \implies 180 = 2 ( 3x )$

$\sf \implies 3x = \dfrac{180}{2}$  

$\sf \implies 3x = 90$

$\sf \implies x = \dfrac{90}{3}$

$\sf \implies x = 30$

Therefore ,  

Breadth = x = 30  

Length = 2x = 60  

_____________

Verification :-  

2( l + b ) = 180  

2( 60 + 30 ) = 180  

2( 90 ) = 180  

180 = 180  

LHS = RHS  

Hence , the answer is correct

Answer 2

$\LARGE\mathfrak{\underline{\underline\textcolor{aqua}{ Given :-}}}$

$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\large\textsf{Length of the rectangle is twice the breadth}$

$\qquad\tt{:}\longrightarrow\large\textsf{Perimeter of the rectangle = 180 units }$

$\large\textsf{ }$

$\LARGE\mathfrak{\underline{\underline\textcolor{aqua}{To \; \; Find :-}}}$

$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\large\textsf{Dimensions of the rectangle = ?}$

$\large\textsf{ }$

$\LARGE\mathfrak{\underline{\underline\textcolor{aqua}{Formula :-}}}$

$\large\textsf{ }$

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

$\large\textsf{ }$

$\LARGE\mathfrak{\underline{\underline\textcolor{aqua}{Solution :-}}}$

$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\large\textsf{Let the breadth of rectangle be ' x ' .}$

$\qquad\tt{:}\longrightarrow\large\textsf{So , the length would be ' 2x ' .}$

$\qquad\tt{:}\longrightarrow\large\textsf{Perimeter of the rectangle = 180 units}$

$\large\textsf{ }$

↦ As per the given conditions :-

$\qquad\tt{:}\longrightarrow\large\textsf{2 ( 2x + x ) = 180}$

$\qquad\tt{:}\longrightarrow\large\textsf{4x + 2x = 180 }$

$\qquad\tt{:}\longrightarrow\large\textsf{6x = 180}$

$\qquad\tt{:}\longrightarrow\large\textsf{ x = \cancel{\cfrac{\large\textsf{180}}{\large\textsf{6}}} }$

$\qquad\tt{:}\longrightarrow\boxed{\large\textsf\textcolor{red}{x = 30}}$

$\large\textsf{ }$

∴ Breadth = 30 units

∴ Length = 2 × 30 = 60 units

$\large\textsf{ }$

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$\large\textsf{ }$

$\LARGE\mathfrak{\underline{\underline\textcolor{aqua}{More \; \; Formulas :-}}}$

$\qquad\tt{:}\longrightarrow\large\textsf{ {\large\textsf{L.S.A.}}_{\large\textsf\textcolor{green}{( \; Cuboid \; )}} = \large\textsf{2h ( l + b )} }$

$\qquad\tt{:}\longrightarrow\large\textsf{ {\large\textsf{T.S.A.}}_{\large\textsf{( \; Cuboid \; )}} = \large\textsf{2 ( lb + bh + hl )} }$

$\qquad\tt{:}\longrightarrow\large\textsf{ {\large\textsf{Volume}}_{\large\textsf{( \; Cuboid \; )}} = \large\textsf{l×b×h} }$

__________________________________________________________

$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\large\textsf{ {\large\textsf{L.S.A.}}_{\large\textsf\textcolor{green}{( \; Cube \; )}} = \large\textsf{4×l²} }$

$\qquad\tt{:}\longrightarrow\large\textsf{ {\large\textsf{T.S.A.}}_{\large\textsf{( \; Cube \; )}} = \large\textsf{6 × l²} }$

$\qquad\tt{:}\longrightarrow\large\textsf{ {\large\textsf{Volume}}_{\large\textsf{( \; Cube \; )}} = \large\textsf{l²} }$

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$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\large\textsf{ {\large\textsf{C.S.A.}}_{\large\textsf\textcolor{green}{( \; Cylinder \; )}} = \large\textsf{2 × πrh} }$

$\qquad\tt{:}\longrightarrow\large\textsf{ {\large\textsf{T.S.A.}}_{\large\textsf{( \; Cylinder \; )}} = \large\textsf{2πr × ( r + h )} }$

$\qquad\tt{:}\longrightarrow\large\textsf{ {\large\textsf{Volume}}_{\large\textsf{( \; Cylinder \; )}} = \large\textsf{πr²h} }$

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$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\large\textsf{ {\large\textsf{C.S.A.}}_{\large\textsf\textcolor{green}{( \; Cone \; )}} = \large\textsf{πrl} }$

$\qquad\tt{:}\longrightarrow\large\textsf{ {\large\textsf{T.S.A.}}_{\large\textsf{( \; Cone \; )}} = \large\textsf{πr × ( r + l )} }$

$\qquad\tt{:}\longrightarrow\large\textsf{ {\large\textsf{Volume}}_{\large\textsf{( \; Cone \; )}} } \large\textsf{ = \cfrac{\large\textsf{1}}{\large\textsf{3}} }\large\textsf{× πr²h}$

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$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\large\textsf{ {\large\textsf{T.S.A.}}_{\large\textsf\textcolor{green}{( \; Sphere \; )}} = \large\textsf{4πr²} }$

$\qquad\tt{:}\longrightarrow\large\textsf{ {\large\textsf{Volume}}_{\large\textsf{( \; Sphere \; )}} } \large\textsf{ = \cfrac{\large\textsf{4}}{\large\textsf{3}} }\large\textsf{× πr³}$

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