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03 Jun 2020, 23:55
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
79% (01:04) correct
21%
(01:11)
wrong
based on 122
sessions
History
Date
Time
Result
Not Attempted Yet
What is the area of rectangle ABCD?
(1) The length of side AB is 2 units more than the length of side BC.
(2) The length of the diagonal AC is 10 units.
(1) The length of side AB is 2 units more than the length of side BC.
(2) The length of the diagonal AC is 10 units.
yashikaaggarwal
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04 Jun 2020, 00:35
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IMO C
Statement 1 : l=b+2
Area = l*b = (b+2)*b =? (Insufficient)
Statement 2: 10^2=l^2+b^2
100=l^2+b^2 =? (Insufficient)
1&2 together.
100 = l^2+b^2
100 = (b+2)^2+b^2
100 = b^2+4+4b+b^2.
96 = 2b^2+4b
48 = b^2+2b => 48 = b(b+2)
6*8 = b(l)
Length = 8 and breadth= 6.
Area of rectangle = 6*8= 48 (sufficient)
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Statement 1 : l=b+2
Area = l*b = (b+2)*b =? (Insufficient)
Statement 2: 10^2=l^2+b^2
100=l^2+b^2 =? (Insufficient)
1&2 together.
100 = l^2+b^2
100 = (b+2)^2+b^2
100 = b^2+4+4b+b^2.
96 = 2b^2+4b
48 = b^2+2b => 48 = b(b+2)
6*8 = b(l)
Length = 8 and breadth= 6.
Area of rectangle = 6*8= 48 (sufficient)
Posted from my mobile device
04 Jun 2020, 00:42
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Bunuel
Solution
Step 1: Analyse Question Stem
- • We need to find the area of rectangle ABCD.
- o Area of a rectangle \(= length * breadth = AB*BC\)
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: The length of side AB is 2 units more than the length of side BC.
- • \(AB = BC + 2\)
• So, \(Area = AB*BC = (BC+2)*BC\)
• However, we don’t know BC so we cannot find the area.
Statement 2: The length of the diagonal AC is 10 units.
- • It means, \(AB^2 + BC^2 = 10^2\)
• But we cannot find AB and BC from here and hence we cannot find AB*BC
Step 3: Analyse Statements by combining.
From statement 1: \(AB – BC = 2\)
From statement 2: \(AB^2 + BC^2 =10^2\)
On combining the two statements, we can write,
- • \((AB – BC)^2 = 4 ⟹ AB^2 + BC^2 – 2AB*BC = 4 ⟹10^2 - 2AB*BC = 4\)
Thus, the correct answer is Option C.
