Question

The length and breadth of a rectangle are in the ratio 7:4. If its perimeter is 440 m. Find its dimension and area.​

Answer 1

$\large\sf\underline{Given}$

• Ratio of length and breadth of rectangle = 7 : 4

• Perimeter of the rectangle = 440m

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$\large\sf\underline{To\:find}$

• Dimension of rectangle .

• Area of rectangle .

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$\large\sf\underline{Assuming}$

• Length of the rectangle = 7x

• Breadth of the rectangle = 4x

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$\large\sf\underline{Solution}$

We know ,

$\small{\underline{\boxed{\mathrm\pink{\: Perimeter\:of\:the\: rectangle=2(l+b)}}}}$

$\sf➞\:2(l+b)=Perimeter$

Substituting the value :

$\sf➞\:2(7x+4x)=440m$

$\sf➞\:2(11x)=440m$

$\sf➞\:22x=440m$

$\sf➞\:x=\frac{440m}{22}$

$\small{\underline{\boxed{\mathrm\purple{➛\:x=20\:m}}}}$

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Now substituting the value of x and y in :

$\sf\:Length=7x$

$\sf➞\: Length=7 \times 20$

$\small{\underline{\boxed{\mathrm\purple{➛\: Length=140\:m}}}}$

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And ,

$\sf\:Breadth=4x$

$\sf➞\:Breadth=4 \times 20$

$\small{\underline{\boxed{\mathrm\purple{➛\: Breadth=80\:m}}}}$

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So the area of the rectangle :

$\sf\: Length \times Breadth$

$\sf➞\:140\:m\:\times 80\:m$

$\small{\underline{\boxed{\mathrm\purple{➛\:11200\:m^{2}}}}}$

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⠀⠀ ${\sf{{\blue{Answers:}}}}$

⠀Dimensions :

⠀⠀⠀‎‎⠀⠀➠ length = 140m

⠀⠀⠀‎‎⠀⠀➠ breadth = 80

⠀➠ Area = 11200 sq.m

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!! Hope it helps !!