Question

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.

Answer 1

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

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.

Answer 2

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