It is currently 14 Dec 2018, 11:24

### 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

# QOTD # 9 The length of a leg of an isosceles right triangle

Author Message
TAGS:
Moderator
Joined: 18 Apr 2015
Posts: 5175
Followers: 77

Kudos [?]: 1035 [2] , given: 4660

QOTD # 9 The length of a leg of an isosceles right triangle [#permalink]  13 Sep 2016, 05:52
2
KUDOS
Expert's post
00:00

Question Stats:

60% (02:01) correct 39% (01:01) wrong based on 33 sessions
 Quantity A Quantity B The length of a leg of an isosceles right triangle with area R The length of a side of a square with area R

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Practice Questions
Question: 9
Page: 204
[Reveal] Spoiler: OA

_________________
Moderator
Joined: 18 Apr 2015
Posts: 5175
Followers: 77

Kudos [?]: 1035 [0], given: 4660

Re: QOTD # 9 The length of a leg of an isosceles right triangle [#permalink]  13 Sep 2016, 05:55
Expert's post
Explanation

In an isosceles right triangle, both legs have the same length. The area of an isosceles right triangle with legs of length x is equal to $$\frac{x^2}{2}$$ The area of a square is $$s^2$$ . Since you are given that an isosceles right triangle and a square have the same area R, it follows that $$\frac{x^2}{2}=s^2$$ and so $$x=\sqrt{2}s$$

Since $$\sqrt{2}$$ is greater than 1, the length of a leg of the triangle is greater than the length of a side of the square.

The correct answer is Choice A
_________________
GRE Instructor
Joined: 10 Apr 2015
Posts: 1242
Followers: 46

Kudos [?]: 1129 [1] , given: 7

Re: QOTD # 9 The length of a leg of an isosceles right triangle [#permalink]  12 Apr 2018, 08:58
1
KUDOS
Expert's post
Carcass wrote:
 Quantity A Quantity B The length of a leg of an isosceles right triangle with area R The length of a side of a square with area R

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

The length of a leg of an isosceles right triangle with area R
Let x = the length of one leg
Since this is an isosceles right triangle, the length of the other leg must also be x
Also, since this is a right triangle, then the base has length x AND the height is x

Area of triangle = (base)(height)/2
So, we can write: R = (x)(x)/2
Simplify: R = x²/2
Multiply both sides by 2 to get: 2R = x²
Take square root of both sides to get: √(2R) = x

Great, we have now written Quantity A in terms of R

The length of a side of a square with area R
Let y = the length of one side of square
So, we can write: R = (y)(y)
Simplify: R = y²
Take square root of both sides to get: √R = y

We have now written Quantity B in terms of R

So, we now have the following:
Quantity A: √(2R)
Quantity B: √R

At this point, we may recognize that Quantity A is greater.
However, if you need more convincing, we can take √(2R) and REWRITE it as (√2)(√R) to get:
Quantity A: (√2)(√R)
Quantity B: √R

Now divide both quantities by √R to get:
Quantity A: √2
Quantity B: 1

Since √2 ≈ 1.4, we can see that Quantity A is greater

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

Manager
Joined: 26 Jan 2018
Posts: 172
Followers: 0

Kudos [?]: 104 [0], given: 3

Re: QOTD # 9 The length of a leg of an isosceles right triangle [#permalink]  12 Apr 2018, 09:49
When the question says one of the legs of the triangle, does that mean it is one of the 2 equal sides of the isosceles triangle? Can it not be the 3rd side?
GRE Instructor
Joined: 10 Apr 2015
Posts: 1242
Followers: 46

Kudos [?]: 1129 [2] , given: 7

Re: QOTD # 9 The length of a leg of an isosceles right triangle [#permalink]  12 Apr 2018, 09:54
2
KUDOS
Expert's post
mohan514 wrote:
When the question says one of the legs of the triangle, does that mean it is one of the 2 equal sides of the isosceles triangle? Can it not be the 3rd side?

Good question.

In a right triangle, the two sides that form the 90-degree angle are called legs.
The remaining (and longest) side is called the hypotenuse.

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

Re: QOTD # 9 The length of a leg of an isosceles right triangle   [#permalink] 12 Apr 2018, 09:54
Display posts from previous: Sort by