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In the figure, if AB = 10, what is the length of the side CD
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23 Mar 2019, 08:49
23 Mar 2019, 08:49
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60% (02:25) correct
39% (01:54) wrong based on 23 sessions
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#GREpracticequestion In the figure, if AB = 10.jpg [ 19.65 KiB | Viewed 5705 times ]
In the figure, if AB = 10, what is the length of the side CD
A. \(5\)
B. \(5 \sqrt{3}\)
C. \(\frac{10}{\sqrt{3}}\)
D. \(10\)
E. \(10 \sqrt{3}\)
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Re: In the figure, if AB = 10, what is the length of the side CD
[#permalink]
07 Jun 2020, 00:39
07 Jun 2020, 00:39
This problem is based on Similar Triangles. [Refer attached Image]
Now, two triangles are similar when all of their angles are equal.
Let's find out all angles of these two triangles. [Refer attached Image]
Now, we know that all angles of these two triangles are equal, that means they are similar triangles
=> Triangle ACB ~ Triangle ECD and we know that
"If two triangles are similar then their corresponding sides are in the same ratio"
=> \(\frac{AC}{EC}\) = \(\frac{BC}{CD}\)
Let's find out AC using Pythagoras theorem
\(AB^2\) = \(AC^2\) + \(BC^2\)
\(10^2\) = \(AC^2\) + \(5^2\)
\(AC^2\) = 100 - 25 = 75
AC = \(\sqrt{75}\) = 5\(\sqrt{3}\)
Using \(\frac{AC}{EC}\) = \(\frac{BC}{CD}\)
CD = \(\frac{BC*EC}{AC}\) = \(\frac{5*10}{5\sqrt{3}}\)
CD = \(\frac{10}{\sqrt{3}}\)
So, Answer is C
Hope it helps!
Now, two triangles are similar when all of their angles are equal.
Let's find out all angles of these two triangles. [Refer attached Image]
Now, we know that all angles of these two triangles are equal, that means they are similar triangles
=> Triangle ACB ~ Triangle ECD and we know that
"If two triangles are similar then their corresponding sides are in the same ratio"
=> \(\frac{AC}{EC}\) = \(\frac{BC}{CD}\)
Let's find out AC using Pythagoras theorem
\(AB^2\) = \(AC^2\) + \(BC^2\)
\(10^2\) = \(AC^2\) + \(5^2\)
\(AC^2\) = 100 - 25 = 75
AC = \(\sqrt{75}\) = 5\(\sqrt{3}\)
Using \(\frac{AC}{EC}\) = \(\frac{BC}{CD}\)
CD = \(\frac{BC*EC}{AC}\) = \(\frac{5*10}{5\sqrt{3}}\)
CD = \(\frac{10}{\sqrt{3}}\)
So, Answer is C
Hope it helps!
Attachments
image-1.jpg [ 59.97 KiB | Viewed 3545 times ]
gmatclubot
Re: In the figure, if AB = 10, what is the length of the side CD [#permalink]
07 Jun 2020, 00:39
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