Page 65 - Mathematics Class - XII

ACTIVITY 4.5

OBJECTIVE
To find the time when the area of a rectangle of given dimensions become maximum, if the length is decreasing
and the breadth is increasing at given rates.

MATERIAL REQUIRED
Y Chart paper Y Scale Y Eraser
Y Paper cutter Y Pencil Y Cardboard

PRE-REQUISITE KNOWLEDGE
1. Knowledge of the concept of rate change.
2. Knowledge of the concept optimization of a function.

PROCEDURE

1. Take a rectangle A of dimensions 24 cm × 12 cm.
1
2. Let the length of the rectangle is decreasing at the rate of 1cm / s and the breadth is increasing at the rate
of 2 cm / s.
3. Cut other rectangle A , A , A , A , A , A , A , A , A , A , A etc. of dimensions 23 cm × 14 cm,
11
7
6
2
3
12
4
5
9
10
8
22 cm × 16 cm, 21 cm × 18 cm, 20 cm × 20 cm, 19 cm × 22 cm, 18 cm × 24 cm, 17 cm × 26 cm, 16 cm × 28 cm,
15 cm × 30 cm, 14 cm × 32 cm, 13 cm × 34 cm (Fig.(a)).
4. Paste these rectangles on the cardboard.
A 1 12 cm A 2 14 cm A 3 16 cm A 4 18 cm
24 cm 23 cm 22 cm 21 cm
(i) (ii) (iii) (iv)

A 6 22 cm A 7 24 cm A 8 26 cm
A 20 cm
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20 cm 19 cm 18 cm 17 cm
(v) (vi) (vii) (viii)

A 9 28 cm A 10 30 cm A 11 32 cm A 12 34 cm

16 cm 15 cm 14 cm 13 cm
(ix) (x) (xi) (xii)
Fig. (a)

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