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
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Correct Answer: 20 metres
Solution : Given: The perimeter of the top of a rectangular table is 56 metres and its area is 192 m 2 . Use the formulas, Perimeter = $2(l+b)$ Area = $l\times b$ Length of diagonal = $\sqrt{l^2+b^2}$ Where $l$ and $b$ are length and breadth. Here, $2(l+b)=56$ ⇒ $(l+b)=28$ Also, $lb=192$. We know the identity, $a^2+b^2=(a+b)^2-2ab$. ⇒ $l^2+b^2=(l+b)^2-2lb$ Substitute the values in the above equation, ⇒ $l^2+b^2=(28)^2–2\times 192$ ⇒ $l^2+b^2=784–384=400$ The length of its diagonal = $\sqrt{l^2+b^2}$ = $\sqrt{400}$ = 20 m. Hence, the correct answer is 20 metres.
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