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01. The diagonal of a rectangle is thrice its small side. The ratio of the length to the breadth of the rectangle is
A. 3 : 1 B. √3 : 1
C. √2 : 1 D. 2√2 : 1

Answer and Explanation

Answer: 2√2 : 1

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

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02. A took 15 seconds to cross a rectangular field diagonally walking at the rate of 52 m/ min and B took the same time to cross the same field along its sides walking at the rate of 68 m/ min. The area of the field is
A. 30 sq metres B. 40 sq metres
C. 50 sq metres D. 60 sq metres

Answer and Explanation

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

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03. A rectangular carpet has an area of 60 sq m. If its diagonal and longer side together are equal to 5 times the shorter side, then the length of the carpet is
A. 5 m B. 12 m
C. 13 m D. 14.5 m

Answer and Explanation

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

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04. The diagonal of the floor of a rectangular closet is 7 ½ feet. The shorter side of the closet is 4 ½ feet. What is the area of the closet in square feet?
A. 5 ¼ B. 13 ½
C. 27 D. 37

Answer and Explanation

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.

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05. The diagonal of a rectangle is √41 cm and its area is 20 sq cm. The perimeter of the rectangle must be
A. 9 cm B. 18 cm
C. 20 cm D. 41 cm

Answer and Explanation

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

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06. A courtyard 25 m long and 16 m broad is to be paved with bricks of dimensions 20 cm by 10 cm. The total number of bricks required is
A. 18,000 B. 20,000
C. 25,000 D. None of these

Answer and Explanation

Answer: 20,000

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

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07. The length of a rectangle is three times of its width. If the length of the diagonal is 8√10 cm, then the perimeter of the rectangle is
A. 15√10 cm B. 16√10 cm
C. 24√10 cm D. 64 cm

Answer and Explanation

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

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08. A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges?
A. 20
B. 24
C. 30 D. 33

Answer and Explanation

Answer: 30

Explanation:

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09. The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
A. 16 cm B. 18 cm
C. 24 cm D. Data inadequate

Answer and Explanation

Answer: 18 cm

Explanation:

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10. Find the area of a rectangular field if John walking at the speed of 48m/min took 20 seconds to cross the field diagonally and Harry walking at a speed of 72m /min took 15 seconds to cross the field along its sides.
A. 64 B. 144
C. 34 D. Cannot be determined

Answer and 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

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