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Two sides of a triangle have lengths 6 and 8. Which of the f
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30 Nov 2018, 17:28
30 Nov 2018, 17:28
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Two sides of a triangle have lengths 6 and 8. Which of the following are possible areas of the triangle?
I. 2
II. 12
III. 24
A. I only
B. I and II only
C. II and III only
D. I and III only
E. I, II, and III
I. 2
II. 12
III. 24
A. I only
B. I and II only
C. II and III only
D. I and III only
E. I, II, and III
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Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: Two sides of a triangle have lengths 6 and 8. Which of the f
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01 Dec 2018, 15:12
01 Dec 2018, 15:12
1
Carcass wrote:
Two sides of a triangle have lengths 6 and 8. Which of the following are possible areas of the triangle?
I. 2
II. 12
III. 24
A. I only
B. I and II only
C. II and III only
D. I and III only
E. I, II, and III
I. 2
II. 12
III. 24
A. I only
B. I and II only
C. II and III only
D. I and III only
E. I, II, and III
Area of triangle = (base)(height)/2
Let's let the side with length 8 be the base.
So, to MAXIMIZE the area of the triangle, we must MAXIMIZE the height of the triangle.
This occurs when the side with length 6 is PERPENDICULAR to the side with length 8
In this case, area of triangle = (8)(6)/2 = 24
So, the greatest possible area = 24
Conversely, to MINIMIZE the area of the triangle, we must MINIMIZE the height of the triangle.
Well, if we keep decreasing the angle between the two given sides, we can make the height as small as we want.
In fact, we could make the height equal 1 or 0.1 or even 0.0000000000000001
So, the area of the triangle must be greater than 0 and less than or equal to 24
In other words 0 < (area of triangle) ≤ 24
So, the area COULD be 2 or 12 or 24
Answer: E
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Re: Two sides of a triangle have lengths 6 and 8. Which of the f
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13 Jan 2023, 02:34
13 Jan 2023, 02:34
Hello from the GRE Prep Club BumpBot!
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
