Question

The area of rectangular field is 10092sqm its length is three times as long as it width find its perimeter

Answer 1

Required Solution :

›» Perimeter = 464 m

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How to solve?

• Here as we are given that area of rectangular field is 10092 square metre and its length is three times as long as it width. So, at first we'll find the length and width.

• In order to calculate length and width, we'll form a suitable equation.To form a suitable equation, we'll assume the width as "x" and then its length becomes "3x" [as per the question].

• Then after calculating width and length ,we'll substitute the values in the formula of perimeter of square to calculate its perimeter.

So, let's solve!!

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Given:

• Area of the rectangular field = $\sf { {10092 \: m}^{2} }$

• Length = three times as long as it width.

To calculate:

• Perimeter of the field.

Calculation:

In order to calculate perimeter, we'll calculate measure of its length and width.

Let the width of the field be "x m".

›» As the question says that length is three times as long as it width. Thus,

→ Length = 3 × width

→ Length = 3 × x

→ Length = 3x m

Now, as we know that :

›» Area of rectangle = length × breadth

But, according to the question :

→ 10092 = x × 3x

→ 10092 = 3$\sf{{x}^{2}}$

→ $\sf{\dfrac{10092}{3} = {x}^{2}}$

→ 3364 = $\sf{{x}^{2}}$

→ √3364 = x

→ 58 = x

Thus,

• Width ⇒ x ⇒ 58 m
• Length ⇒ 3x ⇒ 3 × 58 ⇒ 174 m

Now, as we know that,

›» Perimeter of rectangle = 2 ( l + b )

Inserting values,we get :

→ Perimeter = 2 ( 174 + 58 )

→ Perimeter = 2 × 232

→ Perimeter = 464 m

Therefore, perimeter of the rectangular park is 464 m.