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# In the diagram below, triangle ABC is right-angled at B. D and E are

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Math Expert
Joined: 02 Sep 2009
Posts: 53771
In the diagram below, triangle ABC is right-angled at B. D and E are  [#permalink]

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17 Jul 2017, 23:32
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Difficulty:

45% (medium)

Question Stats:

67% (01:54) correct 33% (02:19) wrong based on 48 sessions

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In the diagram below, triangle ABC is right-angled at B. D and E are points on AC and AB, respectively. If BC = 6, what is the area of triangle BPC?

(1) BE = BC and BD bisects ∠ABC.
(2) AB = 8.

Attachment:

2017-07-18_1031.png [ 8.11 KiB | Viewed 768 times ]

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In the diagram below, triangle ABC is right-angled at B. D and E are  [#permalink]

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18 Jul 2017, 01:21
Bunuel wrote:
In the diagram below, triangle ABC is right-angled at B. D and E are points on AC and AB, respectively. If BC = 6, what is the area of triangle BPC?

(1) BE = BC and BD bisects ∠ABC.
(2) AB = 8.

Attachment:
2017-07-18_1031.png

It should be A.

Statement 1: Sufficient

(1) BE = BC and BD bisects ∠ABC.

If BE = BC, then BP splits the triangle BEC in two equal halves. We know sides of the triangle BEC so we can calculate its area.

For BEC,
$$Area = \frac{1}{2}*base*height = \frac{1}{2}*6*6 = 18.$$

For BPC
$$Area = \frac{1}{2} * 18 = 9.$$

Statement 2: Insufficient

(2) AB = 8.

With this information, we can calculate area of triangle ABC but with no information on points D, E or P, we have no way of calculating area of the triangle.
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Joined: 21 Mar 2016
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Re: In the diagram below, triangle ABC is right-angled at B. D and E are  [#permalink]

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19 Jul 2017, 00:04
lets take the easier statement2 first
stat2: not suff,,,we can calculate the area of triangle ABC..nothing else..

stat1: traingle BEC is isosceles and the angle bisector is the median as well,,, hence PE = PC.
median divides the traingle into two equal are... hence suff

ans A
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Re: In the diagram below, triangle ABC is right-angled at B. D and E are  [#permalink]

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01 Mar 2019, 11:10
Another way of looking at 1) From BE=BC and angle bisector BD we know the 2 divided triangles have an equal side and angle. Since they share side BP they also have another equal side (SAS congruent, so each is half the area of EBC).
Re: In the diagram below, triangle ABC is right-angled at B. D and E are   [#permalink] 01 Mar 2019, 11:10
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