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
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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