Question

the length of a rectangular field is 8m less than twice it's breadth if the perimeter of the rectangular field is 56 meters find the length of its sides

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Answer 1

Answer:

L=16

B=12

Step-by-step explanation:

L=(2B-8)

Perimeter= 2(L+B)=56

2(2B-8)+2(B)=56

6B-16=56

B=72/6=12

L=16

Answer 2

The sides of the rectangular field are :

• The length of the field = 16 m.
• The breadth of the field = 12 m.

Given :

• The length of the field is 8 m less than twice it's breadth.
• The perimeter of the rectangular field = 56 m.

To Find :

• The length and the breadth of the field.

Solution :

Let,

The breadth of the field be x.

The length of the field be 2x – 8 because according to the question, the length of the field is 8 m less than twice it's breadth.

We know that,

Perimeter of rectangle = 2(l + b)

Where,

★ l = length

★ b = breadth

Given,

★ Perimeter of the field = 56 m.

$:\implies \rm 56 \: m = 2 \bigg((2x - 8 \: m) + x \bigg) \\ \\ :\implies \rm 56 \: m = 2(2x - 8 \: m+ x) \\ \\ :\implies \rm \dfrac{56}{2} \: m= 2x + x - 8 \: m\\ \\ :\implies \rm 28 \: m = 3x - 8 \\ \\ :\implies \rm 28 \: m + 8 \: m = 3x \\ \\ :\implies \rm 36 \: m = 3x \\ \\ :\implies \rm \dfrac{36}{3} \: m = x \\ \\ :\implies \rm 12 \: m = x \\ \\ \: \: \therefore \: \: \rm x = 12 \: m$

So, the length and the breadth of the field are :

● Breadth of the field = x = 12 m.

● Length of the field = 2x – 8 = 2(12 m) – 8 = 2 × 12 – 8 m = 24 – 8 m = 16 m.

Hence,

The sides of the field are 12 m and 16 m.