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M28-18

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New post 16 Sep 2014, 01:29
1
7
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

48% (01:19) correct 52% (01:31) wrong based on 89 sessions

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New post 16 Sep 2014, 01:29
Official Solution:

What is the area of a region enclosed by \(|\frac{x}{3}|+|\frac{y}{9}|=10\)?

A. \(675\)
B. \(1350\)
C. \(2700\)
D. \(5400\)
E. \(10800\)


Find the \(x\) and \(y\) intercepts.

When \(y=0\), then \(x=30\) or \(x=-30\).

When \(x=0\), then \(y=90\) or \(x=-90\).

So, we have 4 points: (30, 0), (-30, 0) (0, 90), (0, -90). When joining these points we get the rhombus:

Image

The area of a rhombus is \(\frac{d_1*d_2}{2}\) (where \(d_1\) and \(d_2\) are the lengths of the diagonals), thus the area of the enclosed figure is \(\frac{60*180}{2}=5,400\).


Answer: D
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Re: M28-18  [#permalink]

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New post 16 Oct 2016, 23:24
Hello,

Why we not considered the figure square ?

Is it because,in square, the four pieces of diagonals from the point of intersections are all equal. But here they are not ?

Please explain the reasoning.

Thanks
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New post 17 Oct 2016, 03:12
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Re: M28-18  [#permalink]

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New post 17 Oct 2016, 09:56
Bunuel wrote:
karant wrote:
Hello,

Why we not considered the figure square ?

Is it because,in square, the four pieces of diagonals from the point of intersections are all equal. But here they are not ?

Please explain the reasoning.

Thanks


If you refer to the image you'd see that the figure is NOT a square (the diagonals are not equal).



Got it. Thanks Bunuel !!
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New post 11 May 2018, 22:46
Hi Karan,

More reliable way to find out whether this is square or not is to know the fact that, when the Rise/Run is equal i.e 10/10 or 25/25 in otherwords where the Slope is 1, we end up with 45-45-90 triangle. we add up all the four 45-45-90 triangle we end up with square, in this example clearly the Rise/Run is not 1. Hence it is a Rhombus and not a square.
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M28-18  [#permalink]

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New post 01 Nov 2018, 09:49
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In case you don't have the equation for the area of a rhombus memorized, you could have also multiplied the area of a triangle by 4. This figure is made up of 4 equal triangles.
Area of triangle = 1/2bh
Area of our figure=4*(1/2*30*90)=5400
Answer=D.
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M28-18   [#permalink] 01 Nov 2018, 09:49
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