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# What is the perimeter of rhombus ABCD? (1) Area of ABCD is

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What is the perimeter of rhombus ABCD? (1) Area of ABCD is [#permalink]  15 Sep 2005, 15:54
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What is the perimeter of rhombus ABCD?

(1) Area of ABCD is 140cm^2

(2) Diagonal BD is 48 meters
VP
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C.

i) Area = 140 cm2
we cannot find side of the rhombus unless we know its hieght; therefore insufficient.

ii) rhombus diagonals are of different length. unless we know both diagonals we cannot find side.

together:
area = 1/2(d1 + d2)
140 = 1/2(48 + d2)
d2 = 232

as two diagonals in rhombus intersect at right angle (90 degrees)
side = sqrt (116^2 - 24^2)
permeter = side * 4
Manager
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c) both statements together are sufficient.

perimeter = ?

statement I: area of rhombus = 140 cm^2, ie. opposite diagonals (d1 and d2), d1*d2=280. that gives us little info about AB,BC or any other side. Insufficient

statement II: BD=48. Insufficient.

Together, we can calculate AC. Since the diagonals bisect at right angles, we can get each side by using pythagoras theorem.
Manager
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duttsit wrote:
together:
area = 1/2(d1 + d2)

I think area of a rhombus = 1/2(d1*d2) not 1/2(d1+d2)
Senior Manager
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C for the same reasoning as chets.
Manager
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Why Not B - If we take the definition of a rhombus as, "A rhombus is a square with a lean. All sides have equal length, and opposite sides are parallel. Also, opposite angles are equal," then given the length of the diagonal "48" we should be able to find a side of the rhombus. My calculations show that the side is equal to 24 sqrt 2. Perimeter equals 24 sqrt 2 * 4.
_________________

Chet

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chet719 wrote:
Why Not B.
given the length of the diagonal "48" we should be able to find a side of the rhombus. My calculations show that the side is equal to 24 sqrt 2. Perimeter equals 24 sqrt 2 * 4.

Guess you are assumming here that rhombus diagonals are equal in length. It is not true.
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