Question

A rectangle has a length which is 4 feet less than three times the width. The perimeter is 224 feet. What are the dimensions .

Answer 1

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

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

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• Length of rectangle is 4 feet less than three times the width

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• The perimeter is 224 feet

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

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• The dimensions of rectangle

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

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• Let the length of rectangle be "x"

• Let the breadth of rectangle be "y"

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

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Length of rectangle is 4 feet less than three times the width

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➠ x = 3y - 4 ------- (1)

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

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➠ 2(Length + Width) --------(2)

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Also given that the perimeter is 224 feet

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

$\:\:$

• Length = x = 3y - 4

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• Width = y

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• Perimeter = 224

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⟮ Putting these values in (2) ⟯

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➠ 2(Length + Width)

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➜ 2(x + y) = 224

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➜ 2(3y - 4 + y) = 224

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➜ $\sf 4y - 4 = \dfrac { 224 } { 2 }$

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➜ 4y - 4 = 112

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➜ 4y = 112 + 4

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➜ 4y = 116

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➜ $\sf y = \dfrac { 116 } { 4 }$

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➨ y = 29

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• Hence width of rectangle is 29 feet

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⟮ Putting y = 29 in (1) ⟯

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➜ x = 3y - 4

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➜ x = 3(29) - 4

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➜ x = 87 - 4

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➨ x = 83

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• Hence length of rectangle is 83 feet

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∴ The length and width of rectangle is 83 feet & 29 feet respectively

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Additional information

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Area of rectangle

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• Length × Width

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Properties of rectangle

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• Opposite sides are parallel and congruent.

• All angles are right.

• The diagonals are congruent and bisect each other.

• Opposite angles formed at the point where diagonals meet are congruent.

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

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Answer 2

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

$\:\:$

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

$\:\:$

• Length of rectangle is 4 feet less than three times the width

$\:\:$

• The perimeter is 224 feet

$\:\:$

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

$\:\:$

• The dimensions of rectangle

$\:\:$

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

$\:\:$

• Let the length of rectangle be "x"

• Let the breadth of rectangle be "y"

$\:\:$

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

$\:\:$

• Length of rectangle is 4 feet less than three times the width

$\:\:$

➠ x = 3y - 4 ------- (1)

$\:\:$

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

$\:\:$

➠ 2(Length + Width) --------(2)

$\:\:$

Also given that the perimeter is 224 feet

$\:\:$

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

$\:\:$

Length = x = 3y - 4

$\:\:$

Width = y

$\:\:$

Perimeter = 224

$\:\:$

⟮ Putting these values in (2) ⟯

$\:\:$

➠ 2(Length + Width)

$\:\:$

➜ 2(x + y) = 224

$\:\:$

➜ 2(3y - 4 + y) = 224

$\:\:$

➜ $\sf 4y - 4 = \dfrac { 224 } { 2 }$

$\:\:$

➜ 4y - 4 = 112

$\:\:$

➜ 4y = 112 + 4

$\:\:$

➜ 4y = 116

$\:\:$

➜ $\sf y = \dfrac { 116 } { 4 }$

$\:\:$

➨ y = 29

$\:\:$

• Hence width of rectangle is 29 feet

$\:\:$

⟮ Putting y = 29 in (1) ⟯

$\:\:$

➜ x = 3y - 4

$\:\:$

➜ x = 3(29) - 4

$\:\:$

➜ x = 87 - 4

$\:\:$

➨ x = 83

$\:\:$

• Hence length of rectangle is 83 feet

$\:\:$

• ∴ The length and width of rectangle is 83 feet & 29 feet respectively

$\:\:$

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