Question

The length and the breadth of a rectangular park are in the ratio 5:3 and ita perimetre is 128 m. Find the area of the park

Answer 1

$\textbf{\underline{\underline{Answer :-}}}$

The area of the Rectangle is 960 sq.cm

$\textbf{\underline{\underline{Explanation :- }}}$

Given :

Ratio of the Length and Breadth of the Rectangle = 5 : 3

Perimeter of Rectangle = 128 m

To find :

The area of the park

Solution :

Consider the Length as 5x

Consider the Breadth as 3x

$\star$ As we know :

Perimeter of Rectangle =

$\boxed{\sf{ \: \: 2(length + breadth) \: \: }}$

$\star{\sf{\implies{2(5x + 3x) = 128}}}$

$\star{\sf{\implies{10x + 6x = 128}}}$

$\star{\sf{\implies{16x = 128}}}$

$\star{\sf{\implies{x = \dfrac{128}{16}}}}$

$\star{\sf{\implies{ x= 8}}}$

$\boxed{\sf{x = 8}}$

Value of 5x

$\star{\sf{\implies{5 \times x}}}$

$\star{\sf{\implies{5 \times8}}}$

$\star{\sf{\implies{40}}}$

Value of 3x

$\star{\sf{\implies{3 \times x}}}$

$\star{\sf{\implies{3 \times 8}}}$

$\star{\sf{\implies{24}}}$

Length = 40 m

Length = 40 m Breadth = 24 m

$\star$ Area of Rectangle =

$\boxed{\sf{ \: \:length \times breadth\: \: }}$

$\star{\implies{\sf{40 \times 24}}}$

$\star{\implies{\sf{960}}}$

Area of Rectangle = 960 sq.cm

$\therefore$The area of the Rectangle is 960 sq.cm

Answer 2

$\mathfrak {\huge S \blue{ \underline{ \underline{olution \colon}}}}$



$\sf Ratio \: of \: Length \: and \: Breadth = 5 : 3$

Length = 5x

Breadth = 3x

As we know that

Perimeter of Rectangle = 2(L + B)

So,

128 m = 2(5x + 3x)

128 m = 2 × 8x

128 m = 16x

$\dfrac{128}{16}$ = x

8 m = x

________________________________________

Length = 5 × 8 = 40 m
Breadth = 3 × 8 = 24 m

Area of Rectangle = L × B
Area of Rectangle = 40 × 24 m²

Area of Rectangle = $\boxed{\boxed{\sf 960 \: m^2}}$