Answer: 2√2 : 1

Explanation:
√(l2 + b2) = 3b => l2 + b2 = 9b2 => l2= 8b2 => l2/b2 = 8 => l/b = √8 = 2√2:1

Answer: 60 sq metres

Explanation:
Length of the diagonal = (52 * 15/60) = 13m
Sum of length and breadth = (68 * 15/60) = 17 m
Hence √(l2 + b2) = 13 or l2 + b2 = 169 and l + b = 17
Area = lb = ½ (2lb) = ½ [(l + b)2 – (l – b)2] = ½ (289 – 169) = 60 sq m

Answer: 12 m

Explanation:
We have lb = 60 and √(l2 + b2) + l = 5b
Now l2 + b2 = (5b – l)2 => 24b2 – 10lb = 0 => 24b2 – 600 = 0
B2 = 25, b = 5
Hence, l = (60/5) = 12m , So length of the carpet is 12 m

Answer: 27

Explanation:
Other side = √[(15/2)2 – (9/2)2] = √(144/4) = 6 ft
Hence, Area of the closet = (6 * 4.5) = 27 sq feet.

Answer: 18 cm

Explanation:
√(l2 + b2) = √41 or l2 + b2 = 41, Also lb = 20
(l + b)2 = (l2 + b2) + 2lb = 41 + 40 = (l + b) = 9
Hence, Perimeter = 2 (l + b) = 18 cm

Answer: 20,000

Explanation:
Number of Bricks = (Area of the courtyard)/(Area of 1 brick) = (2500 * 1600)/(20 * 10) = 20,000

Answer: 64 cm

Explanation:
Let the breadth be x cm, Then length = 3x cm.
X2 + (3x)2 = (8√10)2 => 10x2 = 640 => x2 = 64 => x = 8
So, length = 24 cm and breadth = 8 cm
Hence, Perimeter = [2 (24 + 8)] cm = 64 cm

Answer: 30

Explanation:

Answer: 18 cm

Explanation:

Answer: 34

Explanation:
The length of the diagonal = speed of John * time = (48/60)*20 = 16m
Sum of the adjacent sides of the field = speed of Harry * time = (72/60)*15 = 18m
Area of the field = (182 - 162) / 2 = 34m²