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# If the area of triangle ABC is 15, side AC has length 10, and segment

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Math Expert
Joined: 02 Sep 2009
Posts: 58445
If the area of triangle ABC is 15, side AC has length 10, and segment  [#permalink]

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23 Aug 2018, 04:12
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15% (low)

Question Stats:

91% (01:01) correct 9% (01:53) wrong based on 28 sessions

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If the area of triangle ABC is 15, side AC has length 10, and segment BD is perpendicular to segment AC, what is the length of segment BD?

A. 9
B. 6
C. 5
D. 3
E. 1.5

Attachment:

image006.jpg [ 2.32 KiB | Viewed 570 times ]

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If the area of triangle ABC is 15, side AC has length 10, and segment  [#permalink]

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23 Aug 2018, 04:21

Given: Area of triangle(ABC) = 15 | Length of side(AC) = 10

The perpendicular to the segment AC, BD is the height of the triangle.
Here, AC is the length of the base. Area = $$\frac{1}{2} * AC * BD = 15$$.

Therefore, the length of the segment BD $$= \frac{15*2}{AC} = \frac{30}{10}$$ = 3(Option D)
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Re: If the area of triangle ABC is 15, side AC has length 10, and segment  [#permalink]

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23 Aug 2018, 07:27
Bunuel wrote:

If the area of triangle ABC is 15, side AC has length 10, and segment BD is perpendicular to segment AC, what is the length of segment BD?

A. 9
B. 6
C. 5
D. 3
E. 1.5

Attachment:
image006.jpg

$$\frac{1}{2}*AC*BD = 15$$

Or, $$10*BD = 30$$

Or, $$BD = 3$$ , Answer must be (D)
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Re: If the area of triangle ABC is 15, side AC has length 10, and segment  [#permalink]

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26 Aug 2018, 19:20
Bunuel wrote:

If the area of triangle ABC is 15, side AC has length 10, and segment BD is perpendicular to segment AC, what is the length of segment BD?

A. 9
B. 6
C. 5
D. 3
E. 1.5

Attachment:
image006.jpg

Since BD is perpendicular to AC and if we consider AC as the base of the triangle, then BD is the height of the triangle. Thus, we have:

½(AC)(BD) = Area of triangle ABC

½(10)(BD) = 15

5(BD) = 15

BD = 3

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Re: If the area of triangle ABC is 15, side AC has length 10, and segment   [#permalink] 26 Aug 2018, 19:20
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