Last visit was: 21 Nov 2024, 12:44 It is currently 21 Nov 2024, 12:44

Close

GRE Prep 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
Your Progress

every week, we’ll send you an estimated GRE 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.

Close

Request Expert Reply

Confirm Cancel
avatar
Manager
Manager
Joined: 22 Jul 2018
Posts: 80
Own Kudos [?]: 105 [1]
Given Kudos: 0
Send PM
Verbal Expert
Joined: 18 Apr 2015
Posts: 30002
Own Kudos [?]: 36336 [0]
Given Kudos: 25927
Send PM
Retired Moderator
Joined: 07 Jan 2018
Posts: 739
Own Kudos [?]: 1447 [0]
Given Kudos: 93
Send PM
avatar
Manager
Manager
Joined: 22 Feb 2018
Posts: 163
Own Kudos [?]: 214 [0]
Given Kudos: 0
Send PM
Re: In right triangle, ABC, the ratio of the longest side to the [#permalink]
1
We have ABC,
And it’s 3 sides are :
AB
BC
AC
Consider AB is the shortest and AC is the longest side so we have :
AB = 3x
BC = ? (Y)
AC = 5x
Because it is a right triangle, we have : AC^2 = BC^2 + AB^2
(5x)^2 = (3x)^2 + y^2 y^2 = 25x^2 - 9x^2 —> y = 4x

Area : 1/2 * AB * BC = 1/2 * 3x * 4x = 6x^2
We have area between 50 and 150 so:
50 < 6x^2 < 150
25 < 3x^2 < 75
8.3 < x^2 < 25
2.88 < x < 5

So the smallest side which is 3x, is between 8.64 and 15.
C, D and E can be answers to this question.
Intern
Intern
Joined: 11 Jan 2020
Posts: 11
Own Kudos [?]: 6 [1]
Given Kudos: 11
Send PM
Re: In right triangle, ABC, the ratio of the longest side to the [#permalink]
1
I made the shortest side a, the longest side b and the remaining side x . We want to find what a would be if the area is between 50 and 150. We know that side b is the hypotenuse as it is the longest side on a right triangle.

a/b = 3/5 ----> 5a = 3b ---> b= 5a/3

We know that the area is the two legs (a and x) divided by 2: xa/2

a^2 + x^2 = b^2 get x in terms of a

a^2 + x^2 = ( 5a/3)^2

a^2 + x^2 = 25a^2/9

x^2 = (25a^2/9) - a^2

x^2 = (25a^2/9) - 9a^2/9

x^2 = 16a^2/9 take the square root ---> x = 4a/3

plug into area formula

(4a/3)(a) (1/2) ----> 4a^2/6 = area

Now we need to solve for a (shortest side) for the upper and lower limits.

4a^2/6 > 50
4a^2 > 300
a^2 > 75
a > sqr 75 (~ 8.7)


4a^2/6 < 150
4a^2 < 900
a^2 < 225
a < 15

From this, we can find that 8.7 < a< 15

The only answers that fall in that range are C (9) and D(12)
User avatar
GRE Prep Club Legend
GRE Prep Club Legend
Joined: 07 Jan 2021
Posts: 5030
Own Kudos [?]: 74 [0]
Given Kudos: 0
Send PM
Re: In right triangle, ABC, the ratio of the longest side to the [#permalink]
Hello from the GRE Prep Club BumpBot!

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.
Prep Club for GRE Bot
Re: In right triangle, ABC, the ratio of the longest side to the [#permalink]
Moderators:
GRE Instructor
84 posts
GRE Forum Moderator
37 posts
Moderator
1111 posts
GRE Instructor
234 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne