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 Your Progress
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Re: Two sides of a triangle have lengths 6 and 8. Which of the f [#permalink]
01 Dec 2018, 15:12
1
This post received KUDOS
Expert's post
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
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
RELATED VIDEO FROM OUR COURSE
_________________
Brent Hanneson – Creator of greenlighttestprep.com Sign up for our free GRE Question of the Dayemails
greprepclubot
Re: Two sides of a triangle have lengths 6 and 8. Which of the f
[#permalink]
01 Dec 2018, 15:12