Question

ड्रा ऑफ द फॉलोइंग शेप्स एट होम सराउंडिंग ट्राएंगल्स प्रोजेक्ट रैक्टेंगुलर 5:00 बजे सर्कुलर टू थ्री ऑब्जेक्ट्स​

Answer 1

Explanation:

Area of the rectangle = l × b (where b = width of the sheet)

Therefore, width b =

Area

l =

500

25 = 20 cm

Perimeter of sheet = 2 × (l + b) = 2 × (25 + 20) cm = 90 cm

So, the width of the rectangular sheet is 20 cm and its perimeter is 90 cm.

EXAMPLE 3 Anu wants to fence the garden in front of her

house (Fig 11.5), on three sides with lengths

20 m, 12 m and 12 m. Find the cost of fencing

at the rate of  150 per metre.

SOLUTION The length of the fence required is the perimeter

of the garden (excluding one side) which is

equal to 20 m + 12 m + 12 m, i.e., 44 m.

Cost of fencing =  150 × 44 =  6,600.

EXAMPLE 4 A wire is in the shape of a square of side 10 cm. If the wire is

rebent into a rectangle of length 12 cm, find its breadth. Which encloses

more area, the square or the rectangle?

SOLUTION Side of the square = 10 cm

Length of the wire = Perimeter of the square = 4 × side = 4 × 10 cm

= 40 cm

Length of the rectangle, l = 12 cm. Let b be the breadth of the rectangle.

Perimeter of rectangle = Length of wire = 40 cm

Perimeter of the rectangle = 2 (l + b)

Thus, 40 = 2 (12 + b)

or

40

2 = 12 + b

Therefore, b = 20 − 12 = 8 cm

The breadth of the rectangle is 8 cm.

Area of the square = (side)2

= 10 cm × 10 cm = 100 cm2

Area of the rectangle = l × b

= 12 cm × 8 cm = 96 cm2

So, the square encloses more area even though its perimeter is the same as that of the rectangle.

EXAMPLE 5The area of a square and a rectangle are equal. If the side of the square is

40 cm and the breadth of the rectangle is 25 cm, find the length of the

rectangle. Also, find the perimeter of the rectangle.

SOLUTION Area of square = (side)2

= 40 cm × 40 cm = 1600 cm2

Fig 11.5

2019-20