Finding the Side Length of a Square Field

The question asks for the side length of a square field given its area. We know the area of the square field is 196 square meters (sqm).

To solve this, we need to recall the formula for the area of a square.

The area of a square is calculated by multiplying the length of one side by itself. If 's' represents the length of one side of the square, the area (A) is given by:

$\text{Area} = \text{side} \times \text{side} = \text{side}^2$

In mathematical terms:

$A = s^2$

We are given that the area $A = 196$ sqm. We need to find the side 's'.

So, we have the equation:

$s^2 = 196$

To find 's', we need to take the square root of the area. The side length must be a positive value.

$s = \sqrt{196}$

Now, we need to find the number that, when multiplied by itself, equals 196. Let's test some common perfect squares or think about numbers whose squares end in 6 (like 4 or 6) or numbers around $\sqrt{196}$. We know $10^2 = 100$ and $20^2 = 400$, so the number is between 10 and 20.

• $11^2 = 121$
• $12^2 = 144$
• $13^2 = 169$
• $14^2 = 196$

So, the square root of 196 is 14.

$s = 14$

The side length of the square field is 14 meters.

Let's look at the given options:

• Option 1: 16 m
• Option 2: 17 m
• Option 3: 14 m
• Option 4: 13 m

Our calculated side length, 14 meters, matches Option 3.

Additional Information on Square Properties and Units

A square is a special type of quadrilateral where all four sides are equal in length, and all four interior angles are right angles (90 degrees).

When dealing with area, the units are always squared (e.g., $m^2$, $cm^2$, $km^2$, $sqm$). This is because area is a measure of two-dimensional space. When you take the square root of an area to find a side length, the unit becomes a linear unit (e.g., m, cm, km).

In this problem, the area is given in square meters (sqm), so the side length is in meters (m).

Understanding the relationship between area and side length is fundamental in geometry and mensuration problems.