Question

The length of diagonal of square field is 220m find the length of a side in meters and the area of the field in hectares

Answer 1

Given : The length of diagonal of square field is 220m.

To find :

1. Length of a side in meters.
2. Area of the field in hectares.

Solution :

We can simply solve this mathematical problem by using the following mathematical process.

To solve this mathematical problem, we have to know the mathematical relationship between the diagonal and side of a square, which is -

Diagonal = Side × √2

Let, the length of the side = x metres

According to the previously mentioned mathematical property, we can write that :

220 = x × √2

110 × 2 = x × √2

x = (110 × 2)/√2

x = 110√2

Length of a side of the square field = 110√2 metres

Area of the square field :

= (Length of side)²

= (110√2)² m²

= 24200 m²

Now, we have to express the area of the square field in hectares unit. So, we need the mathematical relationship between square metre and hectares, which is -

1 m² = 0.0001 hectares

So,

24200m² = 0.0001 × 24200 = 2.42 hectares

Area of the square field = 2.42 hectares

Hence, the length of a side of the square field is 110√2 metres and the area of the square field is 2.42 hectares.

Answer 2

Answer:

Step-by-step explanation:

Given : The length of diagonal of square field is 220m.

To calculate:

1. Length of a side in meters.

2. Area of the field in hectares.

Solution :

The above problem can be solved as follows:

Let us note the relation between the diagonal and the side of a square:

Now, since the Diagonal = Side × √2

Let, the length of the side be x metres

Therefore, from the above relation, we can simply put the values given in the above question:

220 = x × √2

110 × 2 = x × √2

x = (110 × 2)/√2

x = 110√2

Since x was the length of a side of the square field,

.: Length of a side of the square field = 110√2 metres

Area of the square field :

=(Length of side)²

= (110√2)² m²

= 24200 m²

We have got the area of the square field in metres, but the question asks the area in hectares:

Since,

1 m² = 0.0001 hectares

So,

24200m² = 0.0001 × 24200 = 2.42 hectares

Area of the square field = 2.42 hectares

Hence, the length of a side of the square field is 110√2 metres and the area of the square field is 2.42 hectares.

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