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In right triangle ABC shown,
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09 Mar 2022, 03:00
09 Mar 2022, 03:00
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Question Stats:
62% (01:25) correct
37% (02:01) wrong based on 8 sessions
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GRe in the triangle.jpg [ 12.35 KiB | Viewed 1861 times ]
In right triangle ABC shown, \( \overline{CM}\) is the median to the hypotenuse. If AC is 24, and BC is 10, what is the measure of \( \overline{CM}\)?
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13
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Re: In right triangle ABC shown,
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19 Mar 2022, 01:35
19 Mar 2022, 01:35
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Carcass wrote:
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In right triangle ABC shown, \( \overline{CM}\) is the median to the hypotenuse. If AC is 24, and BC is 10, what is the measure of \( \overline{CM}\)?
Show: ::
13
In right traingle ABC;
\(AB^2 = BC^2 + AC^2\)
\(AB^2 = 10^2 + 24^2\)
\(AB = \sqrt{676} = 26\)
Also, if CM is the median then AM = MB = \(\frac{26}{2} = 13\)
Approach 1:
We can use the Theorem: In a right triangle, the median drawn to the hypotenuse has the measure half the hypotenuse.
Therefore, CM = \(\frac{26}{2} = 13\)
Approach 2:
Draw AB' parallel to BC with AB' = BC = 10 and B'B parallel to AC with B'B = AC = 24
Notice that we get a rectangle AB'BC
Property: Diagonals of a rectangle are equal and bisect each other
i.e. CM = MB = B'M = AM = 13
Attachment:
what is the measure of CM.png [ 5.34 KiB | Viewed 1698 times ]
gmatclubot
Re: In right triangle ABC shown, [#permalink]
19 Mar 2022, 01:35
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