Question

area of a rectangular field is 3584 m² and the length and the breadth are in the ratio 7:2, respectively. what is the perimeter of the rectangle?
step by step explanation:​

Answer 1

Answer :

• Perimeter of the rectangular field = 288 m.

Step by Step Explanation :

Given :

• Area of a rectangular field = 3584 m².
• The ratio of the length and the breadth of a rectangular field = 7 : 2.

To Find :

• The perimeter of the rectangular field.

Solution :

We have to find the perimeter of the field.

First, we need to find the length and breadth of the field. For finding the length and the breadth of the rectangular field, we need to find the value of x.

Let,

The length of the field be 7x.

The breadth of the field be 2x.

We know that,

• Area of rectangle = length × breadth.
• Perimeter of rectangle = 2 (length + breadth).

According to the question,

Area of the field = 3584 m²

=> length × breadth = 3584 m²

=> 7x × 2x = 3584 m²

=> 14x² = 3584 m²

=> x² = 3584 / 14 m²

=> x² = 256 m²

=> x = √256 m²

=> x = 16 m

So,

The length of the field = 7x = 7 × 16 m = 112 m.

The breadth of the field = 2x = 2 × 16 m = 32 m.

Now, we will find the perimeter of the field.

Perimeter of rectangle = 2 (length + breadth)

Now, we have,

• Length = 112 m.
• Breadth = 32 m.

Substitute the length and the breadth of the field in the formula.

=> 2 (112 m + 32 m)

=> 2 (144 m)

=> 288 m

Hence,

The perimeter of the rectangular field is 288 m.