The sides of a rectangle are in the ratio 3 : 7 and its area is 1029 m

1.	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» $\mathfrak{\large{\underline{\underline{Answer :-}}}}$ 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.