Question

Write an equation and solve the problem.
The length of a rectangle is 3 cm greater than its width. The perimeter is 24 cm. What are the dimensions
of the rectangle?
width is 3.5; length is 6.5
width is 4; length is 7
width is 4.5; length is 7.5
width is 5; length is 8​

Answer 1

Answer:

Let width be x

Length = 3+x

ATP:

2(3+x+x) = 24

3+2x = 12

2x = 12-3

2x = 9

x = 9/2

x = 4.5

Width is 4.5cm; length is 7.5cm

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Answer 2

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

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

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• The length of a rectangle is 3 cm greater than its width

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• The perimeter is 24 cm

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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 be "x"

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• Let the width be "y"

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

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➠ 2( Length + Breadth ) ------ (1)

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

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⟮ The length of a rectangle is 3 cm greater than its width ⟯

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➠ Length = y + 3

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➠ x = y + 3 ------ (2)

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

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• Length = x = y + 3

• Width = y

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⟮ Putting these values in (1) ⟯

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➠ 2( Length + Breadth )

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➜ 2( y + 3 + y )

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⟮ Given that that perimeter is 24 cm ⟯

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So,

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➜ 2( y + 3 + y ) = 24

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➜ 2(2y + 3) = 24

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➜ 2y + 3 = 12

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➜ 2y = 12 - 3

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➜ 2y = 9

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➜ $\sf y = \dfrac { 9 } { 2 }$

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➨ y = 4.5 ----- (3)

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• Hence the width of rectangle is 4.5 cm

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$\underline{\bold{\texttt{Putting y = 4.5 from (3) to (2) }}}$

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➠ x = y + 3

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➜ x = 4.5 + 3

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➨ x = 7.5

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• Hence length of rectangle is 7.5 cm

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∴ The length and width of rectangle is 7.5 cm & 4.5 cm 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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• A rectangle is a quadrilateral

• The opposite sides are parallel and equal to each other.

• Each interior angle is equal to 90 degrees.

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

• The diagonals bisect each other.

• Both the diagonals have the same length