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What is the area of rectangle ABCD? (1) Diagonal AC is twice as long
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Bunuel
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What is the area of rectangle ABCD? (1) Diagonal AC is twice as long [#permalink] New post  25 Mar 2020, 23:09
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68% (01:36) correct 32% (01:24) wrong based on 82 sessions

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What is the area of rectangle ABCD?

(1) Diagonal AC is twice as long as side CD
(2) Diagonal AC is 0.1 meters longer side AD
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Re: What is the area of rectangle ABCD? (1) Diagonal AC is twice as long [#permalink] New post  26 Mar 2020, 01:00
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Bunuel wrote:
What is the area of rectangle ABCD?

(1) Diagonal AC is twice as long as side CD
(2) Diagonal AC is 0.1 meters longer side AD


Question: Area of Rectangle = l*b = ?

Statement 1: AC = 2b

But diagonal \(= √(l^2+b^2)\)

i.e. \(2b = √(l^2+b^2)\)

i.e. \(4b^2 = (l^2+b^2)\)

i.e. \(3b^2 = (l^2)\)

i.e. \(l = b√3\)

NOT SUFFICIENT

\(Statement 2: Diagonal AC = l+0.1\)

NOT SUFFICIENT

Combining the statements

l+0.1 = 2b

i.e. \(b√3+0.1 = 2b\)

i.e. we get unique value of b as well as l hence

SUFFICIENT

Answer: Option C
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Re: What is the area of rectangle ABCD? (1) Diagonal AC is twice as long [#permalink] New post  28 Sep 2021, 02:49
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Re: What is the area of rectangle ABCD? (1) Diagonal AC is twice as long [#permalink]
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