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# What is x in the diagram below?

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Math Expert
Joined: 02 Sep 2009
Posts: 52902
What is x in the diagram below?  [#permalink]

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02 Jul 2015, 00:56
1
13
00:00

Difficulty:

45% (medium)

Question Stats:

74% (02:25) correct 26% (02:27) wrong based on 211 sessions

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What is x in the diagram below?

A. 12/7
C. 36/7
D. 48/7
E. 72/7

Kudos for a correct solution.

Attachment:

2015-07-02_1254.png [ 9.84 KiB | Viewed 8718 times ]

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Re: What is x in the diagram below?  [#permalink]

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02 Jul 2015, 01:33
5
2
Area of triangle = base*height

In the given figure,
If we consider the side with 12 units as base & height as the one with 3 units, area = 12*3 -------------- (1)
If we consider the side with 7 units as base & height as the one with x units, area = 7*x ----------------(2)

From 1 & 2,
12*3 = 7*x
x = 36/7
Hence C !!
##### General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 52902
Re: What is x in the diagram below?  [#permalink]

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06 Jul 2015, 03:00
Bunuel wrote:
What is x in the diagram below?

A. 12/7
C. 36/7
D. 48/7
E. 72/7

Kudos for a correct solution.

Attachment:
2015-07-02_1254.png

MANHATTAN GMAT OFFICIAL SOLUTION:

You can calculate the area of the triangle, using the side of length 12 as the base:
(1/2)(12)(3) = 18

Next, use the side of length 7 as the base and write the equation for the area:
(1/2)(7)(x) = 18

Now solve for x, the unknown height:
7x = 36
x = 36/7

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Re: What is x in the diagram below?  [#permalink]

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16 Nov 2015, 07:49
Bunuel wrote:
Bunuel wrote:
What is x in the diagram below?

A. 12/7
C. 36/7
D. 48/7
E. 72/7

Kudos for a correct solution.

Attachment:
2015-07-02_1254.png

MANHATTAN GMAT OFFICIAL SOLUTION:

You can calculate the area of the triangle, using the side of length 12 as the base:
(1/2)(12)(3) = 18

Next, use [color=#ff0000]the side of length 7 as the base and write the equation for the area:
(1/2)(7)(x) = 18
[/color]
Now solve for x, the unknown height:
7x = 36
x = 36/7

Hi Bunel,
Could you kindly explain the highlighted portion in detail?
I am not able to understand why you have equated that to 18?
Thanks,
Arun
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Re: What is x in the diagram below?  [#permalink]

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16 Nov 2015, 08:47
1
ArunpriyanJ wrote:
Bunuel wrote:
Bunuel wrote:
What is x in the diagram below?

A. 12/7
C. 36/7
D. 48/7
E. 72/7

Kudos for a correct solution.

Attachment:
2015-07-02_1254.png

MANHATTAN GMAT OFFICIAL SOLUTION:

You can calculate the area of the triangle, using the side of length 12 as the base:
(1/2)(12)(3) = 18

Next, use [color=#ff0000]the side of length 7 as the base and write the equation for the area:
(1/2)(7)(x) = 18
[/color]
Now solve for x, the unknown height:
7x = 36
x = 36/7

Hi Bunel,
Could you kindly explain the highlighted portion in detail?
I am not able to understand why you have equated that to 18?
Thanks,
Arun

In the given triangle with solid lines, the area of the triangle = 0.5*base*height.

Now you need to understand that the height can be from any of the 3 vertices and the base will then be the side to which the height is perpendicular to.

In this case, the line with length 3 is the height for the base with length 12, giving you area of the triangle = 0.5*12*3 = 18

Similarly, for the same triangle, the area will also be = 0.5*7*x ...( as the side with x length is perpendicular to the 'base' with length 7 units).

For a particular triangle, the area MUST be the same irrespective of what base or height combination you choose.

Thus , you equate, 0.5*7*x = 18 ---> x = 36/7.

Hope this helps.
Intern
Joined: 13 Mar 2016
Posts: 5
Re: What is x in the diagram below?  [#permalink]

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31 May 2016, 03:24
I was trying to solve it with the solid line's length=7, will it be more clearly marked in the exam? After going through the solution i realized that they meant the Solid+dotted line length is equal to 7
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Re: What is x in the diagram below?  [#permalink]

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25 Jan 2018, 17:56
Hi Bunuel,

I am confused about what the 7 is referring to. Is 7 the solid line? If so, how are we using that 7 as a base of the imaginary triangle drawn by the dotted lines? Also, why are we able to reference the area of 18 from the triangle with solid lines to help us determine the base of the dotted line triangle? This one is driving me crazy. Thank you in advance for your reply!
Math Expert
Joined: 02 Sep 2009
Posts: 52902
What is x in the diagram below?  [#permalink]

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25 Jan 2018, 19:33
3
frrcattack wrote:
What is x in the diagram below?

A. 12/7
C. 36/7
D. 48/7
E. 72/7

Hi Bunuel,

I am confused about what the 7 is referring to. Is 7 the solid line? If so, how are we using that 7 as a base of the imaginary triangle drawn by the dotted lines? Also, why are we able to reference the area of 18 from the triangle with solid lines to help us determine the base of the dotted line triangle? This one is driving me crazy. Thank you in advance for your reply!

CE = 3;
AC = 7;
AB = 12;
BD = x.

Consider AB as a base of triangle ABC. The are = 1/2*base*height = 1/2*AB*CE = 1/2*12*3 = 18.

Now, consider AC as a base of the SAME triangle ABC. In this case the height is BD (perpendicular from B to extended base AC) The are = 1/2*base*height = 1/2*AC*BD = 1/2*7*x = 18 --> 36/7.

Hope it's clear.

Attachment:

Untitled.png [ 11.59 KiB | Viewed 3643 times ]

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Re: What is x in the diagram below?  [#permalink]

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25 Jan 2018, 19:48
Bunuel wrote:
frrcattack wrote:
What is x in the diagram below?

A. 12/7
C. 36/7
D. 48/7
E. 72/7

Hi Bunuel,

I am confused about what the 7 is referring to. Is 7 the solid line? If so, how are we using that 7 as a base of the imaginary triangle drawn by the dotted lines? Also, why are we able to reference the area of 18 from the triangle with solid lines to help us determine the base of the dotted line triangle? This one is driving me crazy. Thank you in advance for your reply!

CE = 3;
AC = 7;
AB = 12;
BD = x.

Consider AB as a base of triangle ABC. The are = 1/2*base*height = 1/2*AB*CE = 1/2*12*3 = 18.

Now, consider AC as a base of the SAME triangle ABC. In this case the height is BD (perpendicular from B to extended base AC) The are = 1/2*base*height = 1/2*AC*BD = 1/2*7*x = 18 --> 36/7.

Hope it's clear.

Attachment:
Untitled.png

Wow... thank you Bunuel! Makes much more sense.
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Re: What is x in the diagram below?  [#permalink]

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25 Jan 2018, 22:39
1
Bunuel wrote:
What is x in the diagram below?

A. 12/7
C. 36/7
D. 48/7
E. 72/7

Kudos for a correct solution.

Attachment:
The attachment 2015-07-02_1254.png is no longer available

I solved it this way...

Triangle DBA is Similar to triangle CEA
So, $$\frac{3}{x} = \frac{7}{12}$$, $$x = \frac{36}{7}.$$
Attachments

Untitled.png [ 11.59 KiB | Viewed 3399 times ]

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Joined: 11 Sep 2015
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What is x in the diagram below?  [#permalink]

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19 Apr 2018, 13:51
1
Top Contributor
Bunuel wrote:
What is x in the diagram below?

A. 12/7
C. 36/7
D. 48/7
E. 72/7

Kudos for a correct solution.

Attachment:
2015-07-02_1254.png

I added some letters to help guide the solution.

Area of triangle = (1/2)(base)(height)
IMPORTANT CONCEPT: we can use ANY of the three sides as our base.

So, for example, if we want to find the area of triangle ABC, we can use side AB as the base, or we can use side AC as the base, or we can use side BC as the base.

If we use side AB as the base, then the base has length 12 and the height is 3
So, area of triangle ABC = (1/2)(12)(3)

If we use side AC as the base, then the base has length 7 and the height is x
So, area of triangle ABC = (1/2)(7)(x)

IMPORTANT: If we use side AB as the base, the area of the triangle will be the same as the area we get if we use side AC as the base.

So, (1/2)(12)(3) = (1/2)(7)(x) [solve for x]
Divide both sides by 1/2 to get: (12)(3) = (7)(x)
Divide both sides by 7 to get: 36/7 = x

Cheers,
Brent
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What is x in the diagram below?  [#permalink]

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19 Apr 2018, 18:15
OA: C

Sin A =$$\frac{3}{7}=\frac{x}{12}$$
x=$$\frac{36}{7}$$

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What is x in the diagram below?   [#permalink] 19 Apr 2018, 18:15
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