Selina Concise Class 7 Math Chapter 20 Mensuration Exercise 20A Solution
EXERCISE 20A
(1) Perimeter = 2 × (135 + 65)m
= 2 × 200 m = 400m
Rate of fencing = Rs 60/m
∴Total cost of fencing = Rs (400 × 60) = Rs 24000
(2) Let the length will be 7x m and breadth will be 4x m.
Then, 2 × (7x + 4x) = 440
⇒ 2 × 11x = 440
⇒ 22x = 440
⇒ x = 440/22
⇒ x = 20
Therefore, length = (7 × 20) = 140 m and breadth = (4 × 20) = 80m
Rate of fencing = Rs 150/m
∴ Total cost of fencing = Rs (150 × 440) = Rs 66,000
(3) Let the breadth will be x m.
Applying Pythagoras theorem,
AC2 = AB2 + BC2
⇒ (34)2 = (30)2 + x2
⇒ x2 = (34)2 – (30)2
⇒ x2 = 1156 – 900
⇒ x2 = 256
⇒ x = √256 = 16
Therefore, breadth = 16 m.
∴ Perimeter = 2 × (30 + 16) m
= 2 × 46 m = 92 m
(4) Let the each side will be x m.
Applying Pythagoras theorem,
AC2 = AB2 + BC2
⇒ (12√2)2 = x2 + x2
⇒ (144 × 2) = 2x2
⇒ 2x2 = 288
⇒ x2 = 288/2
⇒ x = √144 = 12
Therefore, length of each side = 12 m
∴ Perimeter = (4 × 12) m = 48 m.
(5) Here, 16 dm = 1.6 m
∴ Perimeter = 2 × (22.5 + 1.6) m
= 2 × 24.1 m = 48.2 m
(6) Let the breadth will be x cm.
Applying Pythagoras theorem,
AC2 = AB2 + BC2
⇒ (25)2 = (24)2 + x2
⇒ x2 = (25)2 – (24)2
⇒ x2 = 625 – 576
⇒ x = √49 = 7
Breadth = 7 cm
∴ Perimeter = 2 × (24 + 7) cm
= 2 × 31 cm = 62 cm
(7) Let the length and the breadth will be 5x and 3x m respectively.
Perimeter = 2 × (5x + 3x) m = (2 × 8x) m = 16x m
Rate of fencing = Rs 48/m
Total cost of fencing = Rs (16x × 48) = Rs 768x
But given = Rs 19200
∴ 768x = 19200
⇒ x = 19200/768
⇒ x = 25
Therefore, Length = (5 × 25) = 125m
And breadth = (3 × 25) = 75 m
(8) Perimeter of square shape = (4 × 20) cm = 80 cm
Let the breadth of rectangular shape be x cm.
Then, Perimeter of rectangular shape = 2 × (24 + x) cm
Then, 2 × (24 + x) = 80
⇒24 + x = 80/2
⇒ x = 40 – 24 = 16
Therefore, breadth = 16 cm.
(9) P = perimeter, Length = l and breadth = b
(i) P = 2 × (l + b)
⇒ P = 2 × (38 + 27)
⇒ P = 2 × 65 = 130 cm
(ii) 2 × (l + b) = P
⇒ (24 + b) = 88/2
⇒ b = 44 – 24
⇒ b = 20
(iii) 2 × (l + b) = P
⇒ l + 28 = 96/2
⇒ l = 48 – 28
⇒ l = 20
(10) Let the length of each side will be x m.
Perimeter = 4x m
Rate of fencing = Rs 75/m
Total cost of fencing = Rs (4x × 75)
But given = Rs 67500
∴ 4x × 75 = 67500
⇒ 4x = 67500/75
⇒ 4x = 900
⇒ x = 900/4
⇒ x = 225
Hence, the side of square = 225m.
(11) Perimeter of rectangular field = 2 × (36 + 28) cm
= 2 × 64 cm = 128 cm
Given, its perimeter = perimeter of a square
Let the length of each side will be x cm.
Then, its perimeter = 4x cm
∴ 4x = 128
⇒ x = 128/4
⇒ x = 32
Very helpful
Very helpful and thanks a lot