## S. K. Gupta Anubhuti Gangal Class 5 Math Fifteenth Chapter Perimeter And Area Exercise 51

## EXERCISE 51

**PERIMETER:** *The word perimeter is derived from two Greek words peri meaning around and metron meaning measure.*

**(1) Find the perimeter of a square with side length:**

(a) 14 cm = (4 × 14) cm = 56 cm

(b) 6 mm = (4 × 6) cm = 24 cm

(c) 4.7 m = (4 × 4.7) m = 18.8 m

(d) 2.17 km = (4 × 2.17) km = 8.68 km

(e) 8.9 cm = (4 × 8.9) cm = 35.6 cm

(f) 0.19 m = (4 × 0.19) m = 0.76 m

**(2) Find the perimeter of a rectangle given:**

(a) Length = 8 cm, Breadth = 5 cm

Solution: Perimeter = [2 × (8+5)] cm = (2 × 13) cm = 26 cm

(b) Length = 16 m, Breadth = 14 m

Solution: Perimeter = [2 × (16+14)] m = (2 × 30) m = 60 m

(c) Length = 7 mm, Breadth = 2.5 mm

Solution: Perimeter = [2 × (7+2.5)] m = (2 × 9.5) mm = 19 mm

(d) Length = 6.4 cm, Breadth = 36 mm

Solution: Here, 6.4 cm = (6.4 × 10) mm = 64 m

Perimeter = [2 × (64+36)] mm = (2 × 100) mm = 200 mm

(e) Length = 1.5 m, Breadth = 70 cm

Solution: Here, 1.5 m = (1.5 × 100) cm = 150 cm

Perimeter = [2 × (150+70)] cm = (2 × 220) cm = 440 cm

(f) Length = 12.1 km, Breadth = 3.2 km

Solution: Perimeter = [2 × (12.1+3.2)] km = (2 × 15.3) km = 30.6 km

**(3) How many meters of fencing are required to enclose a rectangular vegetable garden 15 m long and 6.5 m wide?**

Solution: Fencing of the rectangular garden = [2 × (15+6.5)] m = (2 × 21.5) m = 43 m

**(4) Mr. Chopra wants to put a wooden border around a painting. If the length of the painting is 40 cm and breadth is 25 cm, what will be the cost of putting the border at Rs 40 per meter?**

Solution: Perimeter of the painting = [2 × (40+25)] cm

= (2 × 65) cm = 130 cm = 1.3 m

∴ Cost of the putting = Rs (1.3 × 40) = Rs 52

**(5) How much lace will be needed to put around a square cushion of side 65 cm? What will be the cost of the lace required, if the lace costs Rs 8 per m?**

Solution: Perimeter of the square cushion = (4 × 65) cm = 260 cm = 2.6 m

∴ The required lace costs = Rs (2.6 × 8) = Rs 20.80

**(6) A rope of length 24 m was used to fence off a square patch of land for a garden. Find the length of the side of the square garden.**

Solution: The required length = (24 ÷ 4) m = 6 m

**(7) The following diagram shows a rectangle and a square with dimensions given.**

(a) What is the perimeter of each figure?

Solution: Perimeter of rectangular = [2 × (5+20)] cm = 50 cm

Perimeter of square = (4 × 6) cm = 24 cm

(b) Which figure has a greater perimeter and by how much?

Solution: The greater perimeter = perimeter of rectangular – perimeter of square

= (50 – 24) cm = 26 cm

Hence, the rectangular figure is 26 cm greater than square figure.

**(8) Fill in the blanks in the given table:**

**(9) Find the length of a side of a square whose perimeter is:**

(a) 12 cm

Solution: Length of the square = (12 ÷ 4) cm = 3 cm

(b) 10.4 cm

Solution: Length of the square = (10.4 ÷ 4) cm = 2.6 cm

(c) 36 m

Solution: Length of the square = (36 ÷ 4) m = 9 m

(d) 7.2 m

Solution: Length of the square = (7.2 ÷ 4) m = 1.8 m

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