Page 68 - Mathematics Class - XII

ACTIVITY 4.6

OBJECTIVE

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

MATERIAL REQUIRED
Y Chart paper Y Eraser

Y Paper cutter Y Cardboard
Y Scale Y Glue
Y Pencil

PRE-REQUISITE KNOWLEDGE
1. Knowledge of the concept of maximum value of a function.

2. Knowledge of the concept optimization of a function.

PROCEDURE
1. Take a cardboard of a convenient size and paste a white paper on it.
2. Make rectangles each of perimeter say 44 cm on a chart paper. Rectangles of different dimensions are as
follows:

A 1 7 cm A 2 8 cm A 3 9 cm A 4 9.5 cm

15 cm 14 cm 13 cm 12.5 cm
{i} {ii} {iii} {iv}

A 10 cm A 11 cm A 11.5 cm
5 6 7

12 cm 11 cm 10.5 cm
{v} {vi} {vii}
Fig. (a)

A : 15 cm × 7 cm, A : 14 cm × 8 cm, A : 13 cm × 9 cm, A : 12.5 cm × 9.5 cm
4
3
2
1
A : 12 cm × 10 cm, A : 11 cm × 11 cm, A : 10.5 cm × 11.5 cm
5 6 7
3. Cut out these rectangles and paste them on the white paper on the cardboard {see Fig. (a) [i] to [vii]}.
4. Repeat step 2 for more rectangles of different dimensions each having perimeter 44 cm.
5. Paste these rectangles on cardboard.

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