Question

The sides of a rectangular plot are in the ratio 5 : 4 and its area is equal to 500 m2 . The perimeter of the plot is (A) 80 m (B) 100 m (C) 90 m (D) 95 m​

Answer 1

Answer:

$\Large\Longrightarrow\textbf{Perimeter\:=\:90\:m}$

Given:

$\Large\odot\:\:\textbf{Ratio\:of\:sides\:=\:5:4}$

$\Large\odot\:\:\textbf{Area\:of\:park\:=\: 500\:m^2 }$

Explanation:

$\large\textsf{Let\:the\:ratio\:of\:sides\:be\:x}$

$\large\textsf{Length=\:5\timesx}$

$\large\textsf{Breadth=\:4\timesx}$

$\Large\boxed{\textbf{Area\:of\:rectangle\:=\:Length\timesbreadth\: {units}^2 }}$

$\large\textsf{Area= 5x\times4x }$

$\large\textsf{Area= 20x^2 }$

$\Large\textbf{ATQ,}$

$\large\textsf{ 20x^2\:=\:500\:m^2 }$

$\Large\textbf{Dividing\:both\:sides\:by\:20}$

$\large\textsf{ x^2\:=\:25\:m^2 }$

$\Large\textbf{Square\:rooting\:both\:sides}$

$\large\textsf{x= \sqrt{25\:m^2} }$

$\large\textsf{x=5\:m}$

$\large\textbf{Length= 4\times5 \:m}$

$\large\textbf{Length=20\:m}$

$\large\textbf{Breadth= 5\times5 \:m}$

$\large\textbf{Breadth=25\:m}$

$\Large\boxed{\textbf{Perimeter\:=\:2(l+b)\:units}}$

$\large\textsf{2(25+20)\:m}$

$\large\textsf{2\times45\:m}$

$\large\textsf{90\:m\:or\:option\:C}$

$\Large\boxed{\textbf{Perimeter=90\:m}}$

Answer 2

Let the length of rectangular plot = 5x

and breath of rectangular plot = 4x

area of rectangular plot = 500

$= l \times b = 500 \\ = 5x \times 4x = 500 \\ = 20 {x}^{2} = 500 \\ {x}^{2} = \frac{500}{20 } \\ {x}^{2} = 25 \\ {x}^{2} = {5}^{2} \\ x = 5$

Length = 5 × 5 = 25m

Breadth = 4 × 5 = 20m

Perimeter of rectangular plot = 2(L+B)

= 2(25+20)

= 2 × 45

= 90cm