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Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  In the diagram above, if the area of triangle LNO is 32, then what is

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

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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 ]

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

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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

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

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

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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

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Re: In the diagram above, if the area of triangle LNO is 32, then what is  [#permalink]

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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]

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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.

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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
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