Question

hahalf the perimeter of the of a rectangular room is 46 metre and its length is 6 more than its blood to what is the length and breadth of the room​

Answer 1

Correct Question

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Half the perimeter of rectangular room is 46 metre and its length is 6 more than its breadth what is the length and breadth of the room.

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$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

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$\large{\green{\underline \bold{\tt{Given :-}}}}$

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• Half the perimeter of rectangular room is 46 m

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• Length is 6 more than its breadth

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$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

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• Length and breadth of the room

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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• Let the length be "x"

• Let the breadth be "y"

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$\purple{\underline \bold{According \: to \: the \ question :}}$

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➠ x = y + 6 ---------- (1)

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$\underline{\bold{\texttt{Perimeter of rectangle :}}}$

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➠ 2(Length + Breadth) ------ (2)

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$\underline{\bold{\texttt{Perimeter of rectangular room :}}}$

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• Length = x = y + 6

• Breadth = y

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$\underline{\bold{\texttt{Putting these values in (2) }}}$

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2(Length + Breadth)

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➠ 2(x + y)

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➠ 2(y + 6 + y)

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Given that half the perimeter is 46

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So,

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➜ $\sf 46 = \dfrac { 2(y + 6 + y) } { 2 }$

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➜ 46 = y + 6 + y

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➜ 46 - 6 = y + y

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➜ 40 = 2y

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➨ y = 20 ------- (3)

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• Hence breadth of rectangular room is 20 m

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$\underline{\bold{\texttt{Putting y = 20 from (3) to (1) }}}$

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➠ x = y + 6

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➜ x = 20 + 6

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➨ x = 26

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• Hence length of rectangular room is 26 m

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∴ The length and breadth of rectangular room is 26 m & 20 m respectively.

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Additional information

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Area of rectangle = Length × Breadth

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Properties of rectangle

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• The opposite sides are parallel and equal to each other

• Each interior angle is equal to 90°

• The sum of all the interior angles is equal to 360°

• The diagonals bisect each other

• Both the diagonals have the same length

Answer 2

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$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

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$\large{\green{\underline \bold{\tt{Given :-}}}}$

$\:\:$

• Half the perimeter of rectangular room is 46 m

$\:\:$

• Length is 6 more than its breadth

$\:\:$

$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

$\:\:$

• Length and breadth of the room

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

Let the length be "x"

Let the breadth be "y"

$\:\:$

$\purple{\underline \bold{According \: to \: the \ question :}}$

$\:\:$

➠ x = y + 6 ---------- (1)

$\:\:$

$\underline{\bold{\texttt{Perimeter of rectangle :}}}$

$\:\:$

➠ 2(Length + Breadth) ------ (2)

$\:\:$

$\underline{\bold{\texttt{Perimeter of rectangular room :}}}$

$\:\:$

Length = x = y + 6

Breadth = y

$\:\:$

$\underline{\bold{\texttt{Putting these values in (2) }}}$

$\:\:$

2(Length + Breadth)

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➠ 2(x + y)

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➠ 2(y + 6 + y)

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• Given that half the perimeter is 46

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So,

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➜ $\sf 46 = \dfrac { 2(y + 6 + y) } { 2 }$

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➜ 46 = y + 6 + y

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➜ 46 - 6 = y + y

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➜ 40 = 2y

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➨ y = 20 ------- (3)

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• Hence breadth of rectangular room is 20 m

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$\underline{\bold{\texttt{Putting y = 20 from (3) to (1) }}}$

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➠ x = y + 6

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➜ x = 20 + 6

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➨ x = 26

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• Hence length of rectangular room is 26 m

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• ∴ The length and breadth of rectangular room is 26 m & 20 m respectively.

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