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In the rhombus ABCD, the length of diagonal BD is 6 and the length of

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In the rhombus ABCD, the length of diagonal BD is 6 and the length of  [#permalink]

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New post 28 Oct 2014, 09:20
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Tough and Tricky questions: Geometry.



In the rhombus ABCD, the length of diagonal BD is 6 and the length of diagonal AC is 8. What is the perimeter of ABCD?

A. 10
B. 14
C. 20
D. 24
E. 28

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Re: In the rhombus ABCD, the length of diagonal BD is 6 and the length of  [#permalink]

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New post 28 Oct 2014, 21:21
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Answer = B

Rhombus has equal sides, diagonals bisect each other at \(90^{\circ}\)

Refer diagram below
Attachment:
rhom.png
rhom.png [ 3.05 KiB | Viewed 43820 times ]


\(One side = \sqrt{3^2 + 4^2} = 5\)

Perimeter = 5*4 = 20
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Re: In the rhombus ABCD, the length of diagonal BD is 6 and the length of  [#permalink]

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New post 28 Oct 2014, 10:51
2
1
* Rhombus has all sides equal.
* The diagonals of Rhombus bisect each other at 90 degrees.

Using these 2nd property we can find the side of the Rhombus = 5 (4^2 + 3^2 = 5^2)
Hence, the Perimeter = 5*4 = 20 :)
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Re: In the rhombus ABCD, the length of diagonal BD is 6 and the length of  [#permalink]

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New post 03 Jul 2016, 04:55
PareshGmat wrote:
Answer = B

Rhombus has equal sides, diagonals bisect each other at \(90^{\circ}\)

Refer diagram below
Attachment:
rhom.png


\(One side = \sqrt{3^2 + 4^2} = 5\)

Perimeter = 5*4 = 20

Hi Paresh! I think you meant C not B)
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Re: In the rhombus ABCD, the length of diagonal BD is 6 and the length of  [#permalink]

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New post 31 Dec 2016, 03:51
A rhombus is a parallelogram with four sides of equal length. Thus, AB = BC = CD = DA.

The diagonals of a parallelogram bisect each other, meaning that AC and BD intersect at their midpoints, which we will call E. Thus, AE = EC = 4 and BE = ED = 3. Since ABCD is a rhombus, diagonals AC and BD are also perpendicular to each other.

Labeling the figure with the lengths above, we can see that the rhombus is divided by the diagonals into four right triangles, each of which has one side of length 3 and another side of length 4.

Remembering the common right triangle with side ratio = 3: 4: 5, we can infer that the unlabeled hypotenuse of each of the four triangles has length 5.

Thus, AB = BC = CD = DA = 5, and the perimeter of ABCD is 5 × 4 = 20.

The correct answer is C.
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Re: In the rhombus ABCD, the length of diagonal BD is 6 and the length of  [#permalink]

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New post 31 Dec 2016, 09:13
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Bunuel wrote:

Tough and Tricky questions: Geometry.



In the rhombus ABCD, the length of diagonal BD is 6 and the length of diagonal AC is 8. What is the perimeter of ABCD?

A. 10
B. 14
C. 20
D. 24
E. 28


In a rhombus, the diagonals are perpendicular bisectors.
Image


So, we can add our lengths as follows.
Image

From here, if we focus on one of the 4 right triangles....
Image
...we see we can apply the Pythagorean Theorem to write: 3² + 4² = x²
Evaluate: 9 + 16 = x²
So, 25 = x²
Solve to get: x = 5

Since all 4 sides of a rhombus have equal length, the perimeter = (4)(5) = 20

Answer: C

Cheers,
Brent
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Re: In the rhombus ABCD, the length of diagonal BD is 6 and the length of  [#permalink]

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New post 31 Dec 2016, 09:32
Bunuel wrote:

Tough and Tricky questions: Geometry.



In the rhombus ABCD, the length of diagonal BD is 6 and the length of diagonal AC is 8. What is the perimeter of ABCD?

A. 10
B. 14
C. 20
D. 24
E. 28


\(Perimeter = 2 \sqrt{p^2 + q^2}\)

Or, \(Perimeter = 2 \sqrt{8^2 + 6^2}\)

Or, \(Perimeter = 2 \sqrt{100}\)

Or, \(Perimeter = 2 *10\)

Or, \(Perimeter = 20\)

Thus, correct answer will be (C) 20

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Re: In the rhombus ABCD, the length of diagonal BD is 6 and the length of  [#permalink]

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New post 01 Jun 2017, 13:21
Bunuel wrote:

Tough and Tricky questions: Geometry.



In the rhombus ABCD, the length of diagonal BD is 6 and the length of diagonal AC is 8. What is the perimeter of ABCD?

A. 10
B. 14
C. 20
D. 24
E. 28


We are given the lengths of the diagonals in the rhombus; therefore, all we need to do is plug in both diagonals into the formula for the side length of a rhombus

The Side Length of a Rhombus
\sqrt{(d1)^2 + (d2)^2}/2
\sqrt{(8)^2 + (6)^2}/2
\sqrt{100}/2
10/2=
5 (because a rhombus is an equilateral parallelogram we simply multiply 5 by 4 ( number of the rhombuses sides)

= 20

Thus, "C"
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Re: In the rhombus ABCD, the length of diagonal BD is 6 and the length of  [#permalink]

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Re: In the rhombus ABCD, the length of diagonal BD is 6 and the length of &nbs [#permalink] 02 Jul 2018, 03:09
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