Question

A square field which has side 60 m and a rectangular field with length 80 m have the same perimeter. Which field has the larger area?

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Answer 1

Given

• A square field has a side of 60m
• A rectangular field has a length of 80m
• The square and rectangular field have the same perimeter.

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To Find

• The field with a larger area.

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Solution

With the given value of the side of the square field, we'll first find its perimeter.

Formula to Find Perimeter of Square ⇒ 4 × Side

Side ⇒ 60 m

Perimeter of Square Field ⇒ 4 × 60

Perimeter of Square Field ⇒ 240 m

∴ The perimeter of the square field is 240 m

Now we need to find the breadth of the rectangular field in order to get the area. To do so, we'll use the perimeter of the square obtained and find it using the following equation.

Perimeter of Square Field = Perimeter of Rectangular Field

240 m = 240 m

Perimeter of Rectangle ⇒ 2 (Length + Breadth)

Perimeter of Rectangular Field ⇒ 240 m

Length ⇒ 80 m

Breadth ⇒ x m

Let's solve the below step-by-step to find the value of the breadth.

2 (80 + x) = 240

Step 1: Simplify the equation.

⇒ 2 (80 + x) = 240

⇒ 160 + 2x = 240

Step 2: Subtract 160 from both sides of the equation.

⇒ 160 + 2x - 160 = 240 - 160

⇒ 2x = 80

Step 3: Divide 2 from both sides of the equation.

⇒ 2x ÷ 2 = 80 ÷ 2

⇒ x = 40

∴ The breadth of the rectangular field is 40 m

Now that we have all the required values, let's see which field has a larger area.

Area of Square ⇒ (Side)²

Side ⇒ 60 m

Area of Square Field ⇒ (60)²

Area of Square Field ⇒ 3600 m²

∴ The area of the square field is 3600 m².

Area of Rectangle ⇒ Length × Breadth

Length ⇒ 80 m

Breadth ⇒ 40 m

Area of Rectangular Field ⇒ 80 × 40

Area of Rectangular Field ⇒ 3200 m²

∴ The area of the rectangular field is 3200 m².

Now let's compare the area of both the fields.

3600 m² > 3200 m²

3600 - 3200 = 400

∴ The square field has a larger area by 400m.

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Answer 2

Answer:

Square field has larger area compared to the rectangular field.

Step-by-step explanation:

Given :-

A square field has side 60 m and a rectangular field with length 80 m have the same perimeter.

To find :-

Which field has larger area ?

Solution :-

Perimeter of square:

• 4 × side
• 4 × 60

∴ Perimeter of square = 240 m

Perimeter of rectangular field:

• 2(Length + Breadth)
• 2(80 + Breadth)
• 160 + 2b

∴ Perimeter of rectangle = 160 + 2b

According to the question,

Perimeter of rectangular field = Perimeter of square field

• 160 + 2b= 240
• 2b = 240 - 160
• 2b = 80
• b = 40

∴ Breadth of rectangle = 40 m

Now, we have:

Area of square field = side × side

• 60 × 60
• 3600 m²

Area of rectangular field = Length × Breadth

• 80 × 40
• 3200 m²

3600 m² > 3200 m²

∴ Clearly we can say that square field has larger area compared to the rectangular field.