Question

The perimeter of the rectangle and square are same .Length and breadth of
the rectangle are 10 cm and 8 cm respectively. What is the area of the
square.
(a) 114sq. cm (b) 36sq.cm
(c) 81sq.cm (d) 64sq.cm

Answer 1

Answer:

Given:-

Length and breadth of the

rectangle are 10 cm and 8 cm, perimeter

of the rectangle and square are same.

To find:-

area of the square=?

Solution:-

• So, we have given that perimeter of rectangle and square are same and length and breadth of the rectangle is also given.so first we need to find the perimeter of the rectangle.
• Perimeter of rectangle is = 2(+b)

=2(10+8)

=2(18)

= 36 cm.

• Now, perimeter of square is 4(a),

where a is the side of square.

• We have given that perimeter is

equal so equate 4(a) with the

• perimeter of the rectangle, we get:

4(a) = 36

a = 9 cm

• So the side of the square is 9cm.
• Now area of sqare is 9×9=81.

Answer:-

So the area of the square is

81 cm².

Answer 2

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

$\large\mapsto\texttt{Length of the rectangle = 10cm}\\\\\large\mapsto\texttt{Breadth of the rectangle = 8cm}$

$\LARGE\mathfrak{\underline{\underline{ To \: \: \: Find :-}}}$

$\large\mapsto\texttt{Area of the square = ?}$

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

$\large : \: \Longrightarrow\underline{\boxed{\textsf\textcolor{green}{ Perimeter_{ ( \: Rectangle \: )} = 2 ( l + b ) }}}\\\\\large : \: \Longrightarrow\underline{\boxed{\textsf\textcolor{red}{ Perimeter_{ ( \: Square \: ) } = 4 ( Side ) }}}\\\\\large : \: \Longrightarrow\underline{\boxed{\textsf\textcolor{blue}{ Area_{ ( \: Square \: ) } = Side^{2} }}}$

$\LARGE\mathfrak{\underline{\underline{How \: \: \: to \: \: \: solve :-}}}$

• As it is given that the perimeter of the square is equal to the perimeter of the rectangle.

• We have been provided with the length and breadth of the rectangle , so by using this we can find the perimeter of the rectangle.

• And after finding the perimeter of the rectangle we have to insert that perimeter in the perimeter of the square as the perimeters are the same.

• And from this we can find the side of the square and by using that side we can calculate the area of the square.

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

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$\large:\: \bigstar\textsf\textcolor{orange}{\: \: \: Perimeter_{ ( \: Rectangle \: ) } = 2 ( l + b ) }\\\\\\\large: \: \Longrightarrow\textsf{= 2 ( 10 + 8 ) }\\\\\\\large: \: \Longrightarrow\textsf{= 2 × 18}\\\\\\\large : \: \Longrightarrow\underline{\boxed{\textsf\textcolor{magenta}{ Perimeter_{ ( \: Rectangle \: ) } = 36 \: cm }}}$

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• As it is given that the perimeter of the square I equal to the perimeter of the rectangle. So we have to assume 36cm as the perimeter of the square.

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$\large:\: \bigstar\textsf\textcolor{orange}{\: \: \: Perimeter_{ ( \: Square \: ) } = 4 ( Side ) }\\\\\\\large: \: \Longrightarrow\textsf{36 = 4 ( Side )}\\\\\\\large: \: \Longrightarrow\textsf{ \cfrac{36}{4} = Side }\\\\\\\large : \: \Longrightarrow\underline{\boxed{\textsf\textcolor{violet}{9cm = Side}}}$

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• Now we know the side of the square so we can find the area of the square.

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$\large:\: \bigstar\textsf\textcolor{orange}{\: \: \: Area_{ ( \: Square \: ) } = Side^{2} }\\\\\\\large: \: \Longrightarrow\textsf{= 9²}\\\\\\\large : \: \Longrightarrow\underline{\boxed{\textsf\textcolor{red}{ Area_{ ( \: Square \: ) } = 81\: sq. \: cm }}}$

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$\large : \: \Longrightarrow\underline{\boxed{\textsf\textcolor{blue}{Option ( C ) 81 sq. cm.}}}$

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