Math, asked by andromoboplay, 11 months ago

The sides of a rectangle are in the ratio 3 : 7 and its area is 1029 m². Find the dimensions of the rectangle, and then find its perimeter.

Answers

Answered by Sauron
136

\mathfrak{\large{\underline{\underline{Answer :-}}}}

The Perimeter of the Rectangle is 140 m.

\mathfrak{\large{\underline{\underline{Explanation :-}}}}

Given :

Ratio of the Rectangle sides = 3 : 7

Area of the Rectangle = 1029 m²

To Find :

The dimensions and Perimeter of the Rectangle

Solution :

Consider the Breadth as 3x

Consider the Length as 7x

\purple{\boxed{\sf{\pink{Area = Length \times Breadth}}}}

\tt{\implies} \: 1029 = 7x \times 3x

\tt{\implies} \: 21x^{2} = 1029

\tt{\implies} \: x =  \dfrac{1029}{21}

\tt{\implies} \: x = \sqrt{49}

\tt{\implies} \: x = 7

\rule{300}{1.5}

Value of 3x

\tt{\implies} \: 7 \times 3

\tt{\implies} \: 21

Value of 7x

\tt{\implies} \: 7 \times 7

\tt{\implies} \: 49

Breadth = 21 m

Length = 49 m

\rule{300}{1.5}

Perimeter of Rectangle can be found as the dimensions are given.

\purple{\boxed{\sf{\pink{Perimeter = 2(Breadth+Length)}}}}

\tt{\implies} \: 2(21 + 49)

\tt{\implies} \: 42+ 98

\tt{\implies} \:140

\therefore The Perimeter of the Rectangle is 140 m.


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Answered by Anonymous
22

Let the ratio be x.

3 : 7 = 3x : 7x

Area of rectangle = length × breadth

==> 1029. = 3x ×. 7x

==> 1029. =. 21x²

==> x² = 49

==> x = 7

breadth=7x7=49

length=7x3=21

,perimeter=2(length+breadth)

==> 2(21+49)

==> 2 x70 = 140

perimeter = 140


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