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
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
⇒ a
2
– 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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