Question

Govind and Sanjeev had the adjoining fields shown in (a). Sanjeev suggested that they divide their fields as shown in (b). He said the area of their fields would remain the same but they would spend less money on fencing. Was he right? Give reason. ​

Answer 1

Step-by-step explanation:

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Answer 2

Yes, Sanjeev is correct.

Accordingly the arrangement in fig(b), tha area of both fields remains same but they would have spend less on fencing.

Given:

• Govind and Sanjeev had the adjoining fields shown in (a),see the attached figure.
• Sanjeev suggested that they divide their fields as shown in (b); see the attached figure.
• He said the area of their fields would remain the same but they would spend less money on fencing.

To find:

• Was sanjeev right? Give reason.

Solution:

Concept/formula to be used:

• Perimeter of rectangle: $\bf 2(l + b)$
• Area of rectangle $\bf =lb$ here, l: length and b: breadth
• Area of square=$\bf {a}^{2}$
• Perimeter of square: $\bf 4a$ here, a: side

Step 1:

Find the perimeter of fields of Sanjeev and Govind.

According to the figure (a);

Perimeter of Govind's field$=30 + 45 + 15 + 30 + 15 + 15$

$= 150 \: m$

Similarly,

Perimeter of Sanjeev's field$= 45 + 30 + 15 +15 + 30 + 15$

$= 150 \: m$

Thus,

The perimeter of Govind's and Sanjeev's field is 150 m.

Step 2:

Find the perimeter of both fields in figure 2.

Perimeter of Govind's field$= 4 \times 30$

Perimeter of Govind's field$\bf= 120 \: m$

Similarly,

Perimeter of Sanjeev's field is 120 m.

Thus,

Perimeter of both fields are reduced in the second arrangement and hence cost of fencing will be reduced accordingly.

Step 3:

Find the area of fields.

Govind's field can be divided into one square and one rectangle (see the attached figure 2)

Area of square: $( {15)}^{2} {m}^{2}$

Area of square: $225 \: {m}^{2}$

Length of rectangle:45 m

Breadth of rectangle: 15 m

Area of rectangle $= 45 \times 15$

$= 675 \: {m}^{2}$

Area of Govind's field$= 225 + 675$

Area of Govind's field$\bf= 900 \: {m}^{2}$

Similarly,

The area of sanjeev's field is 900 m².

Step 4:

Find the area of fields in the second arrangement.

According to the figure (b),

Area of Govind and Sanjeev field$= 30 \times 30$

$= 900 \: {m}^{2}$

Thus,

Area of fields of Govind and Sanjeev remians same in both the arrangements.

Final answer:

Sanjeev is correct.

Accordingly the arrangement in fig(b), tha area of both fields remains same but they would have spend less on fencing.

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