Question

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

Answer 1

Answer:

${960m}^{2}$

Step-by-step explanation:

Let the length of the park be 5x meters and the breadth be 3x meters.

∴ perimeter = 2(l + b) = 2(5x + 3x) = 2 × 8x = 16x meters

But, it is given that perimeter = 128m

∴ 16x = 128

⇒ x = 128/16 = 8

∴ length of the park = 5x meters = (5 × 8)m = 40m

breadth of the park = 3x meters = (3 × 8)m = 24m

∴ area of the park = (l × b) sq. units = (40 × 24)sq. m

= 960m^2

Answer 2

$\Large{\underline{\overline{\frak{|~understanding~ the ~Question|}}}}$

Here's the Question that the length and breadth of a rectangular park are in Ratio that is 5:3 and also question says that perimeter of the ratio 5:3 is 128m . then we have to find the area of the park but we have to know the actual length and breadth of Rectangular park to find the area. By using the formulas of Perimeter, We will find the Actual Length & breadth of Rectangular park . Let's find out:

Given:-

• The length and the breadth of a rectangular park are in the ratio 5 : 3
• And their perimeter is 128cm

To Find:

• The Area of the park
• The length & breadth of Rectangular Park

Formula to be Used:

1.

${\boxed{\frak{~perimeter ~of~Rectangle = 2 \times ( length + breadth}}}$

2.

${\boxed{\frak{Area ~of ~Rectangle= length \times breadth}}}$

Solution:

• Area of the park is 960m²
• The length of Rectangular park is 40m
• Breadth of Rectangular park is 24m

Step By Step Explanation:-

⠀

$\sf{Let~ the ~length~ be : 5x }\\ \sf{And~the~breadth ~be : 3x}\\\\\\ \Large\dag~~ {\underline {\frak{as~we ~know~that:} }}$

$\sf\pink{Perimeter~ of~ Rectangle ~= 2 × ( Length~ + ~Breadth)}$

Now,

$\begin{gathered}\: \: :\implies\sf{Perimeter = 2 \times ( Length + Breadth) }\\\\\\ :\implies \sf{2~ \times (5x + 3x) = 128m} \\\\ :\implies \sf { 2 \times 8x= 128m}\\\\ :\implies\sf{16x = 128m }\\\\ :\implies \sf{x = \sf\dfrac{128}{16} }\\\\:\implies{\underline {\boxed{\frak{\pink{ 8cm}}}}}\end{gathered}$

⠀

The length is = 5x × 8 = 5 × 8 = 40cm

The breadth is = 3x × 8 = 3 × 8 = 24cm

⠀

Now, We have to find the Area !

$~~~~~~~~\star ~~{\underline {\boxed{\frak{As ~we ~know~ that:}}}}$

${\frak{Area ~of ~Rectangle= length \times breadth}}$

So,

$\sf{Area ~of ~Rectangle ~= Length ~\times ~Breadth}$

$:\implies\sf{Area ~ = ~~~~~~~~ 40 \times 24}$

$:\implies\sf{Area ~ = ~~~~~~~~ 960m²}$

$\therefore~~{\underline {\frak{\green{~the~area~is ~960m²}}}}$