Question

The length and breadth of a  rectangular park are in the ratio 5:3. If its perimeter is 128 m, find its length.
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Please answer

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Answer 1

Explanation -:

Given :

• Ratio of length and breadth = 5 : 3
• Perimeter of a rectangular park = 128 m

To Find :

• Length of the rectangular park

Solution :

Length and breadth are in a ratio 5 : 3

Let length and breadth be 5x and 3x

$\small \boxed{\rm{ Perimeter \: of \: a \: rectangle = 2(length + breadth)}}$

Perimeter = 128 m

$\small\rm\bf{128 = 2(5x + 3x)}$

$‌⇒\small\rm{ 128 = 2(8x) }$

$⇒\small\rm{ \dfrac{ \cancel{128}}{ \cancel{2}} = 8x }$

$⇒ \small\rm{64 = 8x}$

$⇒ \small\rm{ \dfrac{ \cancel{64}}{ \cancel{8}} = x }$

$\small\boxed{ \rm{x = 8}}$

Length = 5x = 5 × 8 = 40 m

Breadth = 3x = 3 × 8 = 24m

Verifying :

2(5x + 3x) = 128

Putting the value of x = 8

2(5 × 8 + 3 × 8) = 128

2(40 + 24) = 128

2(64) = 128

128 = 128

Hence, proved

$\underline{\rule{70mm}{2pt}}$

Answer 2

Length and breadth are in a ratio 5 : 3

Let length and breadth be 5x and 3x

Perimeter = 128 m

Length = 5x = 5 × 8 = 40 m

Breadth = 3x = 3 × 8 = 24m

Verifying :

2(5x + 3x) = 128

Putting the value of x = 8

2(5 × 8 + 3 × 8) = 128

2(40 + 24) = 128

2(64) = 128

128 = 128

Hence, proved