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# What is the area of rectangular region R ? (1) Each diagonal

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Manager
Joined: 05 Jul 2006
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What is the area of rectangular region R ? (1) Each diagonal [#permalink]  05 Oct 2006, 12:05
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What is the area of rectangular region R ?
(1) Each diagonal of R has length 5.
(2) The perimeter of R is 14.
Director
Joined: 06 Sep 2006
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1 & 2 UNSUFFICIENT

C.

2a + 2b = 14
a + b = 7
a^2 + b^2 = 25

two equations two unknowns.
SVP
Joined: 05 Jul 2006
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What is the area of rectangular region R ?
(1) Each diagonal of R has length 5.
(2) The perimeter of R is 14.

AREA OF RECATANGLE = l*w

diagonal ^2 = l^2+w^2...insuff

L^2+W^2 = 25

paremeter

2(l+w) = 14......insuff AND THE TWO DIMENSIONS = L,7-L

Both together

Manager
Joined: 31 Aug 2006
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I go with (E). Bcoz solving the above 2 eqns. gives 2 values of a. a=3 or a=4.Hence 2 possible values of b. Hence 2 possible values of area.Since we still cannot tell what is the area of the region R.Hence (E)
Intern
Joined: 21 Aug 2006
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Location: LA California
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I will go with C
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Solus Intendo
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Intern
Joined: 14 Jul 2005
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Statement 1: Both diagonals are 5. Only time that will happen is if the rectangle is a square. now lets say each side = a.
Therefore a * Rootover2 (diag of a square) = 5
solve for a and you get the side.
Manager
Joined: 01 Oct 2006
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mukeshnathani wrote:
I go with (E). Bcoz solving the above 2 eqns. gives 2 values of a. a=3 or a=4.Hence 2 possible values of b. Hence 2 possible values of area.Since we still cannot tell what is the area of the region R.Hence (E)

I go with C.

a = 3 or 4
Therefore b = 4 or 3
Hence the sides of the rectangle are 3 and 4 units.
Senior Manager
Joined: 11 May 2006
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mukeshnathani wrote:
I go with (E). Bcoz solving the above 2 eqns. gives 2 values of a. a=3 or a=4.Hence 2 possible values of b. Hence 2 possible values of area.Since we still cannot tell what is the area of the region R.Hence (E)

if a = 3 then b = 4
if a = 4 then b = 3

in both cases area = 12 hence C
Senior Manager
Joined: 11 May 2006
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800_gal wrote:
Statement 1: Both diagonals are 5. Only time that will happen is if the rectangle is a square. now lets say each side = a.
Therefore a * Rootover2 (diag of a square) = 5
solve for a and you get the side.

this is not correct. Even diagonals of a rectangle are equal since opposite sides are equal.
hence both diagonals are sqrt(a^2 + b^2) where a and b are sides of a rectangle.
Director
Joined: 23 Jun 2005
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GMAT 1: 740 Q48 V42
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C

Statement 1:
l^2 + b^2 = 25

INSUFF

Statement 2:

2(l+b) = 14

INSUFF

Together,

(l+b)^2 = l^2 +b^2 +2lb

49 = 25 + 2lb

lb = 12[/b]
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