Question

The sides of a rectangular park are in the ratio 4 : 3. If its perimeter is 392 m, find

its length and breadth​

Answer 1

Given :

• Ratio of length and breadth of a rectangular park = 4 : 3
• Perimeter of rectangular park = 392 m

To find :

• Length
• Breadth

According to the question,

Let,

• The length be 4x
• Breadth be 3x

We know,

• Perimeter of rectangle = 2(l + b)

Where,

• l = length
• b = breadth

Now,

➝ Perimeter of rectangle = 2(l + b)

➝ 392 = 2(4x + 3x)

➝ 392 = 2(7x)

➝ 392 = 14x

➝ 392 ÷ 14 = x

➝ 28 = x

★ Length :

➝ 4x

➝ 4(28)

➝ 112 m

★ Breadth :

➝ 3x

➝ 3(28)

➝ 84 m

So,

• Length = 112 m
• Breadth = 84 m

_____________________

Answer 2

Answer:

Given :-

• The sides of a rectangular park are in the ratio of 4 : 3 and its perimeter is 392 m.

To Find :-

• What is its length and breadth.

Formula Used :-

$\boxed{\bold{\small{Perimeter\: of\: a\: rectangle\: =\: 2(Length + Breadth)}}}$

Solution :-

Let, the length be 4x

And, the breadth will be 3x

According to the question by using the formula we get,

⇒ $\sf 2(4x + 3x) =\: 392$

⇒ $\sf 8x + 6x =\: 392$

⇒ $\sf 14x =\: 392$

⇒ $\sf x =\: \dfrac{\cancel{392}}{\cancel{14}}$

➠ $\sf\bold{\red{x =\: 28\: cm}}$

Hence, the required length and breadth are,

✧ Length = 4x = 4 × 28 = 112 cm

✧ Breadth = 3x = 3 × 28 = 84 cm

$\therefore$ The length and breadth of a rectangular park is 112 cm and 84 cm respectively.

$\rule{300}{1.5}$

Let's Verify :-

↦ $\sf 2(4x + 3x) =\: 392$

↦ $\sf 8x + 6x =\: 392$

Put x = 28 we get,

↦ $\sf 8(28) + 6(28) =\: 392$

↦ $\sf 224 + 168 =\: 392$

↦ $\sf\bold{392 =\: 392}$

➦ LHS = RHS

Hence, Verified ✔