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------------------------------------------------ Of the two square fields, the area of one is 1 hectare, while the other one is broader by 1%. The difference in areas is:

A. 101 sq. metres
B. 201 sq. metres
C. 100 sq. metres
D. 200 sq. metres

Answer :

To find the difference in the areas of the two square fields, we start by understanding the problem:

  1. Initial Information:

    • We have two square fields, let's call them Field A and Field B.
    • The area of Field A is 1 hectare.

  2. Conversion of Units:

    • 1 hectare is equal to 10,000 square meters.
    • Therefore, the area of Field A = 10,000 square meters.

  3. Understanding the Broadened Field:

    • Field B is broader by 1%, which means each side of Field B is 1% longer than a side of Field A.

  4. Side Length Calculation:

    • Let the side of Field A be [tex]s[/tex]. Since the area is 10,000 sq. meters, [tex]s^2 = 10,000[/tex].
    • Therefore, [tex]s = \sqrt{10,000} = 100[/tex] meters.
    • The side of Field B will be [tex]1\%[/tex] longer than Field A, thus:
      [tex]\text{Side of Field B} = s \times 1.01 = 100 \times 1.01 = 101 \text{ meters}[/tex]

  5. Area of Field B:

    • Area of Field B [tex]= (101)^2 \text{ square meters}[/tex]
    • [tex]101^2 = 101 \times 101 = 10,201 \text{ sq. meters}[/tex]

  6. Difference in Areas:

    • Difference [tex]= \text{Area of Field B} - \text{Area of Field A}[/tex]
    • Difference [tex]= 10,201 - 10,000 = 201 \text{ square meters}[/tex]

Therefore, the difference in the areas is 201 square meters.

The correct answer is option B: 201 sq. metres.

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