Last visit was: 30 Apr 2026, 20:27

It is currently 30 Apr 2026, 20:27

Toolkit

Practice Tests

Data Insights Questions

Data Sufficiency (DS)

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
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.

Go to My Error Log Learn more

Request Expert Reply

Confirm Cancel

Back to Forum

Create Topic

What is the area of rectangular region R?

1 2

jabhatta2

Joined: 15 Dec 2016

Last visit: 21 Apr 2023

Posts: 1,251

Own Kudos:

328

Given Kudos: 188

Posts: 1,251

Kudos: 328

21 Apr 2020, 06:06

Kudos

Bookmarks

Bunuel

unceldolan

Bunuel,

isn't this a special Pythagorean triangle? with a,b,c 3,4,5? Hence it would be A not C...

This is a common trap.

Knowing that the hypotenuse equals to 5 DOES NOT mean that the sides of the right triangle necessarily must be in the ratio of Pythagorean triple - 3:4:5. Or in other words: if \(x^2+y^2=5^2\) DOES NOT mean that \(x=3\) and \(y=4\). Certainly this is one of the possibilities but definitely not the only one. In fact \(x^2+y^2=5^2\) has infinitely many solutions for \(x\) and \(y\) and only one of them is \(x=3\) and \(y=5\).

For example: \(x=1\) and \(y=\sqrt{24}\) or \(x=2\) and \(y=\sqrt{21}\)...

Hope this helps.

Hi Bunuel - i thought the answer might be A because

-- the diagonal breaks up the 90 degrees into 2 equal halves (45 degrees each)

hence i thought the diagonal breaks up the rectangle into 2 triangles that are 45-45-90 triangles

hence, i thought this was a special triangle with the ratio of the sides : 1:1 : square root 2

hence you can find the length and breadth

given area is length * breadth = you can then find the area of the rectangle

hence i marked (A) as sufficient

Could you let me know where is the break in my logic

Bunuel

Math Expert

Joined: 02 Sep 2009

Last visit: 30 Apr 2026

Posts: 110,017

Own Kudos:

812,170

Given Kudos: 105,962

Products:

Expert

Expert reply

Posts: 110,017

Kudos: 812,170

21 Apr 2020, 07:06

Kudos

Bookmarks

[email protected]

Bunuel

unceldolan

Bunuel,

isn't this a special Pythagorean triangle? with a,b,c 3,4,5? Hence it would be A not C...

The diagonal of e rectangle bisects the angle ONLY IF the rectangle is a square. If a rectangle is NOT a square, then the diagonal can create an angle with an adjacent side, from 0 to 90, not inclusive.

Eduardo86

Joined: 13 May 2020

Last visit: 19 May 2021

Posts: 27

Own Kudos:

Given Kudos: 182

Location: United Kingdom

Schools: Wharton '23 Kellogg '23

Posts: 27

Kudos: 35

03 Jun 2020, 04:40

Kudos

Bookmarks

Bunuel

Rajeet123

Bunuel

Rajeet123

I had read a formula somewhere which said if any quadrilateral has diagonals intersecting at 90 degrees, then their area can be found out by 1/2 * d1 * d2.
If we use this formula, then A alone is sufficient to answer the question.
Where am I going wrong Bunuel ? Is that formula right?

Do we know that the diagonals intersect at 90 degrees from (1)?

You're right, "rectangular" doesn't necessarily mean a rectangle. Missed that.

No, that's not the point. Rectangular region does mean that the figure is a rectangle. But the diagonals of a rectangle do not always intersect at 90 degrees. This happnes only when a rectangle is a square.

If the two diagonal are the same does not mean the rectangular is a square?

Bunuel

Math Expert

Joined: 02 Sep 2009

Last visit: 30 Apr 2026

Posts: 110,017

Own Kudos:

812,170

Given Kudos: 105,962

Products:

Expert

Expert reply

Posts: 110,017

Kudos: 812,170

03 Jun 2020, 04:57

Kudos

Bookmarks

Eduardo86

Bunuel

Rajeet123

Bunuel

Rajeet123

Do we know that the diagonals intersect at 90 degrees from (1)?

You're right, "rectangular" doesn't necessarily mean a rectangle. Missed that.

If the two diagonal are the same does not mean the rectangular is a square?

The diagonals of any rectangle are equal. So, not, equal diagonal does not necessarily mean that the rectangle is a square.

ScottTargetTestPrep

Target Test Prep Representative

Joined: 14 Oct 2015

Last visit: 30 Apr 2026

Posts: 22,305

Own Kudos:

26,560

[2]

Given Kudos: 302

Status:Founder & CEO

Affiliations: Target Test Prep

Location: United States (CA)

Expert

Expert reply

Posts: 22,305

Kudos: 26,560

[2]

05 Jul 2021, 05:58

Kudos

Bookmarks

Bunuel

What is the area of rectangular region R?

(1) Each diagonal of R has length 5.
(2) The perimeter of R is 14.

Solution:

Question Stem Analysis:

We need to determine the area of region R, which is a rectangle.

Statement One Alone:

Knowing the length of the diagonal of a rectangle is not sufficient to determine its area. For example, if R is a square (recall that a square is also a rectangle), it’s side length would be 5/√2 and its area would be (5/√2)^2 = 25/4. However, R could also be a non-square rectangle with dimensions 3 and 4. In this case, the area of R is 3 x 4 = 12. Statement one alone is not sufficient.

Statement Two Alone:

Knowing the perimeter of a rectangle is not sufficient to determine its area. For example, if R has dimensions 2 and 5, its area is 2 x 5 = 10. However, if R has dimensions 3 and 4, its area is 3 x 4 = 12. Statement two alone is not sufficient.

Statements One and Two Together:

If we let L and W be the dimensions of the rectangle, we can create the equations:

L^2 + W^2 = 5^2

and

2L + 2W = 14

We see that we can solve L and W based on the equations we’ve set up, and once we have the values of L and W, then the area of region R is just the product of L and W. Both statements together are sufficient. (Note: L = 3 and W = 4 OR L = 4 and W = 3. Either way, the area of R is 12.)

Answer: C

bumpbot

Non-Human User

Joined: 09 Sep 2013

Last visit: 04 Jan 2021

Posts: 39,011

Own Kudos:

1,122

Posts: 39,011

Kudos: 1,122

01 Aug 2025, 01:43

Kudos

Bookmarks

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

1 2

Moderators:

Bunuel

Math Expert

110017 posts

kingbucky

498 posts

Gmat860sanskar

212 posts