Question : The perimeter of the top of a rectangular table is 42 metres and its area is 108 metres2. What is the length of its diagonal?
Option 1: 12 metres
Option 2: 15 metres
Option 3: 11 metres
Option 4: 9 metres
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Correct Answer: 15 metres
Solution : According to the question ⇒ Perimeter = 2(length + breadth) = 42 ⇒ Length + breadth = 21 m ⇒ Area = length × breadth = 108 Let the length be a and breadth be (21 – a). ⇒ Area = length × breadth = 108 ⇒ a × (21 – a) = 108 ⇒ a2 – 21 a + 108 = 0 ⇒ (a – 9) (a – 12) = 0 ⇒ a = 9, 12 So, Length = 12 and breadth = 21 – 12 = 9 ⇒ Diagonal = $\sqrt{{length}^2+{breadth}^2}$ = $\sqrt{{12}^2+{9}^2}$ = $\sqrt{{144}+{81}}$ = $\sqrt{{225}}$ = 15 Hence, the correct answer is 15 metres.
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Question : The perimeter of the top of a rectangular table is 56 metres and its area is 192 m2. What is the length of its diagonal?
Option 1: 22 metres
Option 2: 20 metres
Option 3: 16 metres
Option 4: 18 metres
Question : If the sum of the length, breadth and height of a rectangular parallelepiped is 24 cm and the length of its diagonal is 15 cm, then its total surface area is:
Option 1: 256 cm2
Option 2: 265 cm2
Option 3: 315 cm2
Option 4: 351 cm2
Question : The length of two parallel sides of a trapezium are 15 metres and 20 metres. If its height is 22 metres, then what is the area of the trapezium?
Option 1: 295 metre2
Option 2: 385 metre2
Option 3: 425 metre2
Option 4: 315 metre2
Question : The difference between the length and breadth of a rectangle is 40 metres. If its perimeter is 96 metres, then what will be the area of the rectangle?
Option 1: 254 m2
Option 2: 110 m2
Option 3: 176 m2
Option 4: 152 m2
Question : The length of two parallel sides of a trapezium are 25 metres and 30 metres. If its height is 20 metres, then what is the area of the trapezium?
Option 1: 420 m2
Option 2: 350 m2
Option 3: 590 m2
Option 4: 550 m2
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