Question

Q34. The length and the breadth of a
rectangular park are in ratio 5:3 and it's
perimeter is 128cm . Find the area of the park.​

Answer 1

Answer :-

• Area = 960cm²

Given :-

• Length : Breadth = 5 : 3

• Perimeter of Rectangle = 128cm

To Find :-

• The Area of Rectangle.

Step By Step Solution :-

$\boxed{ \sf{ \purple{Perimeter = 2( Length + Breadth)}}}$

$\implies \sf \: 128 = 2(5x + 3x) \\ \\ \implies \sf \: 128 = 16x \\ \\ \implies \sf \cancel\cfrac{128}{16} = x \\ \\ \implies \sf \: x = 8$

Now X = 8

So

Length = 5 × 8 = 40cm ; Breadth = 3 × 8 = 24cm

Now Area ⤵

$\boxed { \sf{ \red{Area = Length \times Breadth}}}$

$\implies \sf \: Area = 40 \times 24 \\ \\ \implies \sf \: Area = 960 {cm}^{2}$

Therefore Area = 960 cm²

__________________________

Answer 2

Answer :-

• Area of the park = 960 cm².

Step by step explanation :-

Given :-

1. Perimeter of the park = 128 cm.
2. Ratio of length and breadth of the park = 5:3.

To find :-

• Area of the park.

Concept :-

• We have given with the ratio of lengh and breadth of the rectangular shape. So, we'll equate the ratio in the form of a variable.

• Then, from the given perimeter, we'll find the dimensions of the rectangular park.

• After calculating the dimensions of the rectangular park, we can easily find out the area of the rectangular park.

Solution :-

☆ Given, ratio of length and breadth = 5:3

∴ let the length of the rectangle (l) be 5x cm.

⇒ breadth of the rectangle (b) = 3x cm.

As we know that :-

Perimeter of the park = 2 ( l + b )

⠀⠀⠀⠀⠀ ⠀ ⠀⠀⠀128 = 2 ( 5x + 3x )

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀128/2 = 8x

⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀8x = 64

⠀⠀⠀⠀ ⠀⠀⠀ ⠀⠀⇒ x = 8 cm

Finding length

5x = 5 × 8 = 40 cm.

Finding breadth

3x = 3 × 8 = 24 cm.

We know that :-

Area of the park = l × b

⠀⠀⠀⠀⠀⠀ ⠀⠀⇒40 × 24

⠀⠀⠀⠀⠀ ⠀⠀⠀⠀ =) 960 cm² ✓

Hence,

• Area of the rectangular park = 960 cm².