Mathematics Lab Activity-11 Class XII

Mathematics Laboratory Activities 11 on Applications of Derivatives for class XI Non-Medical students with complete observation tables strictly according to the CBSE syllabus.

Chapter - 06 

applications of derivatives

Activity - 11

Objective

To verify that amongst all the rectangles of the same perimeter, the square has the maximum area.

Material Required

Chart paper, paper cutter, scale, pencil, eraser cardboard, glue

Procedure

1. Take a cardboard of a convenient size and paste a white paper on it.

Make rectangles each of perimeter say 48 cm on a chart paper. Rectangles of different dimensions are as follows.

Figure 11.1

2. Area of rectangle R₁ : 16 cm x 8 cm = 128 cm².

3. Area of rectangle R₂ : 15 cm x 9 cm = 135 cm².

4. Area of rectangle R₃ : 14 cm x 10 cm = 140 cm².

5. Area of rectangle R₄ : 13 cm x 11 cm = 143 cm².

6. Area of rectangle R₅ : 12 cm x 12 cm = 144 cm².

7. Area of rectangle R₆ : 12.5 cm x 11.5 cm = 143.75 cm².

8. Area of rectangle R₇ : 10.5 cm x 13.5 cm = 141.75 cm².

9. Perimeter of each rectangle is same but their area are  different. Area of rectangle R₅ is the maximum. It is a square of side 12 cm.

Observations

1. Perimeter of each rectangle  R₁,  R₂ , R₃ , R₄, R₅, R₆ , R₇ is  48 cm.

2. Area od rectangles: R₁,  R₂ , R₃ , R₄, R₆ , R₇ all are smaller than the area of rectangle R₅ .

3. Area of rectangle R₅ with dimensions 12 cm x 12 cm is maximum and is equal to 144 cm².

4. In rectangle R₅ , Length = Breadth  ⇒ Rectangle R₅ is a square

Result

Hence it is verified that amongst all the rectangles of same perimeter the square has the maximum area.

Applications

This activity is useful in explaining the idea of maximum of a function.

VIVA – VOICE

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