On a graph the four corners of a certain quadrilateral

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On a graph the four corners of a certain quadrilateral [#permalink]

04 Jan 2013, 03:06

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54% (01:09) wrong

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On a graph the four corners of a certain quadrilateral are (a,5), (b,5), (a,0) and (b,0). If a + c = 12, a < b and both a and b are positive values then what is the area of the quadrilateral?

(1) b + c = 6
(2) The quadrilateral is a rectangle.

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Re: On a graph the four corners of a certain quadrilateral [#permalink]

04 Jan 2013, 03:54

My solution:

Given the information in the question we can already conclude, that the quadriliteral is a rectangle with a width of 5. We need to figure out the length of the rectangle in order to find the area.

(1) with
I) a + c = 12
II) b + c = 6

we can I) - II) => (a-b) = 6

Length = Distance [(a;5) (b;5)] = Distance [(a;0) (b;0)] =
= SQR [ (a-b)^2 + (5-5)^2 ]
= SQR [ 6^2 + 0^2 ]

= 6

=> Area = 6 * 5 = 30 sufficient

(2) We already know that we have a rectangle. The statement gives us no further information about the length. Not sufficent

Hence A

Last edited by trex16864 on 04 Jan 2013, 05:04, edited 2 times in total.

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Re: On a graph the four corners of a certain quadrilateral [#permalink]

04 Jan 2013, 04:41

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trex16864 wrote:

There is a problem with this question. We are given that a + c = 12 and (1) says that b + c = 6, thus a = b + 6, which implies that a > b. But the stem says that a < b. I guess it should be a > b instead of a < b.

In this case the question would be:
On a graph the four corners of a certain quadrilateral are (a,5), (b,5), (a,0) and (b,0). If a + c = 12, a > b and both a and b are positive values then what is the area of the quadrilateral?

Look at the diagram below:

Attachment:

Quadrilateral.PNG [ 9.43 KiB | Viewed 436 times ]

As we can see given quadrilateral is a rectangle and its area = 5*(a-b).

(1) b + c = 6. Since a + c = 12 and b + c = 6, then a - b = 6. Area = 5*6=30. Sufficient.

(2) The quadrilateral is a rectangle. We already know that. Not sufficient.

Answer: A.

Hope it's clear.
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Re: On a graph the four corners of a certain quadrilateral [#permalink] 04 Jan 2013, 04:41

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On a graph the four corners of a certain quadrilateral

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On a graph the four corners of a certain quadrilateral

On a graph the four corners of a certain quadrilateral

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