Question

A perimeter of a rectangle is 72m. Its breadth is 10 m less than its length. find the dimensions of the rectangle.​

Answer 1

Given :

• Perimeter of Rectangle = 72 m
• Breadth is 10 m less than its length .

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To Find :

• Dimensions of the Rectangle = ?

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Solution :

$\large{\dag \; \; {\underline{\pmb{\frak{ Formula \; Used \; :- }}}}}$

${\red{\bigstar}} \; \; {\underline{\boxed{\purple{\sf{ Perimeter{\small_{(Rectangle)}} = 2(Length + Breadth) }}}}}$

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$\large{\dag \; \; {\underline{\pmb{\frak{ According \; to \; the \; Question \; :- }}}}}$

Let the Length be y . So,

$\qquad{\twoheadrightarrow{\sf{ Length = y \; m }}}$

Breadth is 10 m less than the length . So,

$\qquad{\twoheadrightarrow{\sf{ Breadth = y - 10 \; m }}}$

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$\large{\dag \; \; {\underline{\pmb{\frak{ Calculating \; the \; value \; of \; y \; :- }}}}}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { Perimeter = 2(Length + Breadth) } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { 72 = 2 \bigg\{ y + (y - 10) \bigg\} } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { 72 = 2(2y - 10) } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { 72 = 4y - 20 } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { 72 + 20 = 4y } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { 92 = 4y } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { \dfrac{92}{4} = y } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { \cancel\dfrac{92}{4} = y } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; {\qquad{\orange{\sf { Value \; of \; y = 23 }}}} \\ \end{gathered}$

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$\large{\dag \; \; {\underline{\pmb{\frak{ Calculating \; the \; Dimensions \; :- }}}}}$

• ➳ Length = y = 23 m
• ➳ Breadth = y - 10 = 23 - 10 = 13 m

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$\large{\dag \; \; {\underline{\pmb{\frak{ Therefore \; :- }}}}}$

❛❛ Length of the Rectangle is 23 m and its Breadth is 13 m . ❜❜

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Answer 2

As per the data given in the question,

We have to determine the dimension of the rectangle.

From the data,

It is given that,

Perimeter of rectangle = 72 m

As it is given that,

breadth of the rectangle is 10 m less than its length.

So, let the length of rectangle = x m

So, breadth of rectangle $=(x-10)\:m$

So, perimeter of rectangle will be $=2(l+b)$

Now putting the values of l and b and perimeter in above equation,

We will get,

$72=2[(x)+(x-10)]\\=>2x-10 = \frac{72}{2}\\=>2x-10 = 36\\=>2x=36+10\\=>x=\frac{46}{2} = 23\:m$

Hence, value of length of rectangle = x =  23 m

Value of breadth of rectangle = (x -10) = 13 m