It is currently 18 Nov 2018, 23:36

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# DBC is an equilateral triangle/ ABD is an isosceles triangle

Author Message
TAGS:
GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4711
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1615 [1] , given: 376

DBC is an equilateral triangle/ ABD is an isosceles triangle [#permalink]  18 Jan 2016, 02:13
1
KUDOS
Expert's post
00:00

Question Stats:

41% (00:55) correct 58% (01:26) wrong based on 17 sessions

Which of the following statements individually provide(s) sufficient additional information to determine the area of triangle ABC above?

Indicate ALL such statements.

A DBC is an equilateral triangle.
B ABD is an isosceles triangle.
C The length of BC is equal to the length of AD.
D The length of BC is 10.
E The length of AD is 10.

Practice Questions
Question: 23
Page: 336
Difficulty: medium

[Reveal] Spoiler: img
Attachment:

Quant.jpg [ 9.8 KiB | Viewed 6953 times ]
[Reveal] Spoiler: OA

_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4711
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1615 [1] , given: 376

Re: DBC is an equilateral triangle/ ABD is an isosceles triangle [#permalink]  18 Jan 2016, 04:46
1
KUDOS
Expert's post
Solution

From the figure we know that ABC is a right triangle with its right angle at vertex B. You also know that point D is on the hypotenuse AC. You are given that the length of AB is $$10\sqrt{3}$$. However, because the figure is not necessarily drawn to scale, we don’t know the lengths of AD, DC, and BC. In particular, we don’t know where D is on AC.

The area of a triangle is $$\frac{1}{2}(base)(height)$$. Thus, the area of right triangle ABC is equal to 1 of the length of AB times the length of BC. We already know that the length of AB is 103. Any additional information that would allow us to calculate the length of BC would be sufficient to find the area of triangle ABC.

We need to consider each of the five statements individually, as follows.

Statement A: DBC is an equilateral triangle. This statement implies that angle DCB is a 60degree angle; and therefore, triangle ABC is a 30−60−90 degree triangle. Thus the length of BC can be determined, and this statement provides sufficient additional information to determine the area of triangle ABC.

Statement B: ABD is an isosceles triangle. There is more than one way in which triangle ABD can be isosceles. Below are two redrawn figures showing triangle ABD as isosceles. In the figure on the left, the length of AD is equal to the length of DB; and in the figure on the right, the length of AB is equal to the length of AD.

Either of the figures could have been drawn with the length of BC even longer. So, statement B does not provide sufficient additional information to
determine the area of triangle ABC.

Statement C: The length of BC is equal to the length of AD. We have no wayof finding the length of AD without making other assumptions, so statement C does not provide sufficient additional information to determine the area of triangle ABC.

Statement D: The length of BC is 10. The length of BC is known, so the area of triangle ABC can be found. Statement D provides sufficient additional information to determine the area of triangle ABC.

Statement E: The length of AD is 10. The relationship between AD and BC is not known, so statement E does not provide sufficient additional information to determine the area of triangle ABC.

Statements A and D individually provide sufficient additional information to determine the area of triangle ABC. Therefore, the correct answer consists of Choices A and D.

[Reveal] Spoiler: img
Attachment:

Quant.jpg [ 15.83 KiB | Viewed 6972 times ]

_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Intern
Joined: 17 Mar 2018
Posts: 9
Followers: 0

Kudos [?]: 2 [0], given: 7

Re: DBC is an equilateral triangle/ ABD is an isosceles triangle [#permalink]  21 May 2018, 21:01
Can u explain exactly how to use Statement A to find the length of BC?
Re: DBC is an equilateral triangle/ ABD is an isosceles triangle   [#permalink] 21 May 2018, 21:01
Display posts from previous: Sort by

# DBC is an equilateral triangle/ ABD is an isosceles triangle

 Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.