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What is the area of rectangle ABCD? (1) The length of side AB is 2 uni

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Bunuel
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What is the area of rectangle ABCD? (1) The length of side AB is 2 uni [#permalink] New post   03 Jun 2020, 23:55
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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.
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C
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Re: What is the area of rectangle ABCD? (1) The length of side AB is 2 uni [#permalink] New post   04 Jun 2020, 00:35
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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Re: What is the area of rectangle ABCD? (1) The length of side AB is 2 uni [#permalink] New post   04 Jun 2020, 00:42
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Bunuel wrote:
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.


Solution


Step 1: Analyse Question Stem


    • We need to find the area of rectangle ABCD.
      o Area of a rectangle \(= length * breadth = AB*BC\)
    So basically, we need to AB*BC (or the product of any two adjacent sides) of ABCD.

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.
Hence, statement 1 is NOT sufficient and we can eliminate answer Options A and D.

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
Hence, statement 2 is also NOT sufficient and we can eliminate answer Option B.

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,
    • \((AB – BC)^2 = 4 ⟹ AB^2 + BC^2 – 2AB*BC = 4 ⟹10^2 - 2AB*BC = 4\)
Hence, we can find \(AB*BC\).
Thus, the correct answer is Option C.
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Re: What is the area of rectangle ABCD? (1) The length of side AB is 2 uni [#permalink] New post   04 Jun 2020, 00:47
Let length =L
Breadth= B

We have to find: Area of rectangle ABCD= L*B

1) It says: L=B+2
Area= L*B =(B+2)*B= B^2+2B
Not Sufficient

2)It says diagnol AC=10 but tells us nothing about L or B.
Not sufficient

Together 1) and 2) will give us the value of L and B using pythagoras theorm.
Sufficient

Answer: C
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Re: What is the area of rectangle ABCD? (1) The length of side AB is 2 uni [#permalink] New post   04 Jun 2020, 04:36
IMO C

Let length of rectangle be l
breadth be b
Area = l *b

To find Area.

Stmt 1: b =l+2
Area = l*(l+2) INSUFFICIENT

Stmt 2: Diagonal =10
sides cannot be found INSUFFICIENT

Lets combine:

using Pythagoras theorem: Diagonal^2 = l^2 + b^2
10^2 = l^2 + (l+2)^2
i.e. 10^2 = 6^2 + 8^2
l=6, b =8

SUFFICIENT
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Re: What is the area of rectangle ABCD? (1) The length of side AB is 2 uni [#permalink] New post   04 Jun 2020, 21:02
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Bunuel wrote:
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.


Question: Area of rectangle = L*B = ?

Statement 1: L = 2+B

Length of either side is still unknown hence

NOT SUFFICIENT

Statement 2: The length of the diagonal AC is 10 units.

Sides of rectangle may be 6 and 8 or 5√2 each side but both have different areas hence

NOT SUFFICIENT

COmbining the statements

\(L = 2+B\) and \(L^2+B^2 = 10^2\)

Simplification of two equations gives us
L = 8 and B = 6 i.e .Area = 8*6 = 48

SUFFICIENT

Answer: Option C
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Re: What is the area of rectangle ABCD? (1) The length of side AB is 2 uni [#permalink] New post   04 Jun 2020, 21:16
S1: not sufficient since the length and breadth is not known.
S2: Sufficient since the only pythagorean triplet having 10 as the greatest number is 6,8,10.
L-6, B- 8. Therefore , S2 is sufficient.

Correct choice: B

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Re: What is the area of rectangle ABCD? (1) The length of side AB is 2 uni [#permalink] New post   07 Jun 2020, 12:38
Bunuel wrote:
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.


Hi Bunuel,

Can you please tell me where is the issue in my approach.

S1: not sufficient since the length and breadth is not known.
S2: Sufficient since the only pythagorean triplet having 10 as the greatest number is 6,8,10.
L-6, B- 8. Therefore , S2 is sufficient.

Correct choice: B

Thanks,
Ritwik
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Re: What is the area of rectangle ABCD? (1) The length of side AB is 2 uni [#permalink] New post   15 Jun 2020, 07:38
ritwikk2 wrote:
S1: not sufficient since the length and breadth is not known.
S2: Sufficient since the only pythagorean triplet having 10 as the greatest number is 6,8,10.
L-6, B- 8. Therefore , S2 is sufficient.

Correct choice: B

Posted from my mobile device



Can someone point out why my approach is wrong.
Thanks.
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Re: What is the area of rectangle ABCD? (1) The length of side AB is 2 uni [#permalink] New post   01 Aug 2020, 20:01
Unclear why statement 2 isn't sufficient. If we know the diagonal is 10, why can't we apply the 45-45-90 formula and get the lengths of the other sides?
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Re: What is the area of rectangle ABCD? (1) The length of side AB is 2 uni [#permalink]
01 Aug 2020, 20:01
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