GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Oct 2019, 13:03

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

In the diagram above, if the area of triangle LNO is 32, then what is

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58340
In the diagram above, if the area of triangle LNO is 32, then what is  [#permalink]

Show Tags

03 Jan 2016, 13:19
1
4
00:00

Difficulty:

45% (medium)

Question Stats:

66% (01:56) correct 34% (01:56) wrong based on 205 sessions

HideShow timer Statistics

In the diagram above, if the area of triangle LNO is 32, then what is the area of triangle LMN?

A. 24
B. $$24 \sqrt{2}$$
C. $$24 \sqrt{3}$$
D. 32
E. 48

Attachment:

2016-01-04_0017.png [ 10.43 KiB | Viewed 3036 times ]

_________________
Manager
Joined: 09 Jul 2013
Posts: 106
Re: In the diagram above, if the area of triangle LNO is 32, then what is  [#permalink]

Show Tags

04 Jan 2016, 14:55
2
Bunuel wrote:

In the diagram above, if the area of triangle LNO is 32, then what is the area of triangle LMN?

A. 24
B. $$24 \sqrt{2}$$
C. $$24 \sqrt{3}$$
D. 32
E. 48

Even though the figure looks like a square, that can NEVER be assumed. It explicitly states that the figure is not drawn to scale (something we should assume all the time unless it is stated otherwise), and we must ONLY work with the information given.

Examining triangle LNO, we are given that the

$$area= \frac{base * height}{2} = 32$$

Since we have a right angle at O, we can consider the base to be LO and the height to be ON. We are given the height = 8, so the base, LO, is $$\frac{area*2}{base} = \frac{32*2}{8}=8$$

So, triangle LNO is an isosceles right triangle, and therefore the hypotenuse, LN, is $$8\sqrt{2}$$

Now looking at triangle LMN, we have the height given as 6, and the base LN calculated as $$8\sqrt{2}$$, so

$$area=\frac{6*8\sqrt{2}}{2} = 24\sqrt{2}$$

_________________
Dave de Koos
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4001
Re: In the diagram above, if the area of triangle LNO is 32, then what is  [#permalink]

Show Tags

12 Aug 2016, 14:23
Top Contributor
Bunuel wrote:

In the diagram above, if the area of triangle LNO is 32, then what is the area of triangle LMN?

A. 24
B. $$24 \sqrt{2}$$
C. $$24 \sqrt{3}$$
D. 32
E. 48

Attachment:
2016-01-04_0017.png

First examine the blue triangle.

We're told the area = 32
Area = (base)(height)/2
So, 32 = (x)(8)/2
Solve to get: x = 8

Since the blue triangle is a right triangle, we can apply the Pythagorean Theorem to find the length of the hypotenuse.
We get: 8² + 8² = hypotenuse²
Simplify: 128 = hypotenuse²
So, hypotenuse = √128 = 8√2

We get:

At this point, we can focus on the red triangle

We can see that we now have the length of the base AND the height.
So, area of red triangle = (base)(height)/2
= (8√2)(6)/2
= 24√2

RELATED VIDEOS

_________________
Test confidently with gmatprepnow.com
Intern
Joined: 23 Feb 2019
Posts: 1
Re: In the diagram above, if the area of triangle LNO is 32, then what is  [#permalink]

Show Tags

23 Feb 2019, 23:16
Shouldn't the answer be 32 as the two triangles must be congruent and hence have the same area?
Manager
Joined: 09 Jul 2013
Posts: 106
Re: In the diagram above, if the area of triangle LNO is 32, then what is  [#permalink]

Show Tags

24 Feb 2019, 11:53
RanjaniRaghupathi wrote:
Shouldn't the answer be 32 as the two triangles must be congruent and hence have the same area?

Why do you think the two triangles are congruent? We were never told that LMNO is a rectangle. This is a great example of "Note: figure not drawn to scale" being very important.

Remember, no assumptions. Use only the information provided and what can be inferred from it.

Posted from my mobile device
_________________
Dave de Koos
Re: In the diagram above, if the area of triangle LNO is 32, then what is   [#permalink] 24 Feb 2019, 11:53
Display posts from previous: Sort by