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Bunuel
What is the area of rectangle \(ABCD\) ?

(1) The length of diagonal \(AC\) is twice the length of side \(CD\).
(2) The length of diagonal \(AC\) is 0.1 meters longer than the length of side \(AD\).
Solution:
Pre Analysis:
  • We are asked the area of rectangle i.e., the value of \(l\times b\)

Statement 1: The length of diagonal \(AC\) is twice the length of side \(CD\)
  • Diagonal \(=\sqrt{l^2+b^2}\) and side \(CD=b\)
  • According to this statement, \(\sqrt{l^2+b^2}=2b\)
    \(⇒l^2+b^2=4b^2\)
    \(⇒l^2=3b^2\)
    \(⇒l=b\sqrt{3}\)
  • We cannot get the value of \(l\times b\) from this
  • Thus, statement 1 alone is not sufficient and we can eliminate options A and D

Statement 2: The length of diagonal \(AC\) is 0.1 meters longer than the length of side \(AD\)
  • Diagonal \(AC=\sqrt{l^2+b^2}\) and side \(AD=l\)
  • According to this statement, \(\sqrt{l^2+b^2}=0.1+l\)
  • We cannot get the value of \(l\times b\) from this
  • Thus, statement 2 alone is also not sufficient

Combining:
  • From statement 1, \(l=b\sqrt{3}\)
  • From statement 2, \(\sqrt{l^2+b^2}=0.1+l\)
  • Upon combining, we can get the value of l and b separately and get the value of \(l\times b\)as well

Hence the right answer is Option C
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