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# What is the area of rectangle ABCD?

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Math Expert
Joined: 02 Sep 2009
Posts: 58464
What is the area of rectangle ABCD?  [#permalink]

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29 Aug 2018, 01:33
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Difficulty:

25% (medium)

Question Stats:

95% (01:20) correct 5% (00:14) wrong based on 21 sessions

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What is the area of rectangle ABCD?

(1) l^2 + 2lw + w^2 = 16
(2) l^2 – 2lw + w^2 = 4

Attachment:

image004.jpg [ 1.59 KiB | Viewed 620 times ]

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Re: What is the area of rectangle ABCD?  [#permalink]

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29 Aug 2018, 01:42
From statement 1:

L and W can take values (3,1) or (2,2).
Then Area becomes L*W = 3 or 4.
Hence insufficient.

From statement 2:
Only (3,1) or (1,3) satisfies the equation.
2 is sufficient.

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Re: What is the area of rectangle ABCD?  [#permalink]

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29 Aug 2018, 01:51
1
Bunuel wrote:

What is the area of rectangle ABCD?

(1) l^2 + 2lw + w^2 = 16
(2) l^2 – 2lw + w^2 = 4

Attachment:
image004.jpg

(1) l^2 + 2lw + w^2 = 16

(l+w) = 4
several values are possible
3,1 => area = 3
2,2 => area =4

insufficient

(2) l^2 – 2lw + w^2 = 4
(l-w) = 2
again several values are possible
10,8
4,2
5,3

insufficient.

using both

l+w=4
l-w=2

l=3 and w=1
sufficient
C
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What is the area of rectangle ABCD?  [#permalink]

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29 Aug 2018, 02:24
Hi,

Question:
What is the area of rectangle ABCD?

i.e., Area of rectangle = l * w

We need to find the values of l *w or any relation which gives l*w

Statement I is insufficient:

l^2 + 2lw + w^2 = 16

Immediately we can think of (a+b)^2 = a^2 + b^2 + 2ab.

(l+w)^2 = 16.

Taking square root on both sides(side length and area can’t be negative).

l+w = 4

But “l” and “w” can take different values.

l = w = 2. Then the area would be 4.

Or

l = 1 and w = 3. Then the area would be 3.

So insufficient.

Statement II is insufficient:

l^2 – 2lw + w^2 = 4

similar to statement I, it is (a-b)^2 = a^2 + b^2 - 2ab

(l-w)^2 = 4.

Taking square root on both sides(side length and area can’t be negative).

l-w = 2

But “l” and “w” can take different values.

l =4 and w = 2. Then the area would be 8.

Or

l = 3 and w = 1. Then the area would be 3.

We can come up with different values of l and w. So area keep changing.

So insufficient.

Together it is sufficient.

l – w = 2

and l + w = 4

Solving we get l = 3 and w = 1

So, the area of the rectangle has to be 3.

So the answer is C (together sufficient).
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What is the area of rectangle ABCD?   [#permalink] 29 Aug 2018, 02:24
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