GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 09 Dec 2018, 18:05

### 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

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Free GMAT Algebra Webinar

December 09, 2018

December 09, 2018

07:00 AM PST

09:00 AM PST

Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT.
• ### Free lesson on number properties

December 10, 2018

December 10, 2018

10:00 PM PST

11:00 PM PST

Practice the one most important Quant section - Integer properties, and rapidly improve your skills.

# The diagonal of the floor of a rectangular closet is 15/2 feet. The sh

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51035
The diagonal of the floor of a rectangular closet is 15/2 feet. The sh  [#permalink]

### Show Tags

13 Feb 2018, 04:53
00:00

Difficulty:

25% (medium)

Question Stats:

80% (01:53) correct 20% (01:49) wrong based on 70 sessions

### HideShow timer Statistics

The diagonal of the floor of a rectangular closet is 15/2 feet. The shorter side of the closet is 9/2 feet. What is the area of the closet in square feet?

(A) 37

(B) 27

(C) 54/4

(D) 21/4

(E) 5

_________________
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3325
Location: India
GPA: 3.12
The diagonal of the floor of a rectangular closet is 15/2 feet. The sh  [#permalink]

### Show Tags

13 Feb 2018, 06:04
1
Bunuel wrote:
The diagonal of the floor of a rectangular closet is 15/2 feet. The shorter side of the closet is 9/2 feet. What is the area of the closet in square feet?

(A) 37

(B) 27

(C) 54/4

(D) 21/4

(E) 5

In a rectangle, $$Diagonal^2 = Side1^2 + Side2^2$$

$$\frac{225}{4} = \frac{81}{4} + Side2^2$$ -> $$Side2^2 = \frac{144}{4} = 36$$ -> $$Side2= \sqrt{36} = 6$$

Therefore, the Area of the rectangle is $$6*\frac{9}{2}$$ = 27(Option B)
_________________

You've got what it takes, but it will take everything you've got

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4261
Location: United States (CA)
Re: The diagonal of the floor of a rectangular closet is 15/2 feet. The sh  [#permalink]

### Show Tags

14 Feb 2018, 09:57
Bunuel wrote:
The diagonal of the floor of a rectangular closet is 15/2 feet. The shorter side of the closet is 9/2 feet. What is the area of the closet in square feet?

(A) 37

(B) 27

(C) 54/4

(D) 21/4

(E) 5

We can use the Pythagorean theorem to solve for the longer side of the closet:

(9/2)^2 + b^2 = (15/2)^2

81/4 + b^2 = 225/4

b^2 = 144/4

b^2 = 36

b = 6

So the area is 9/2 x 6 = 27.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Senior SC Moderator
Joined: 22 May 2016
Posts: 2197
The diagonal of the floor of a rectangular closet is 15/2 feet. The sh  [#permalink]

### Show Tags

26 Feb 2018, 17:37
Bunuel wrote:
The diagonal of the floor of a rectangular closet is 15/2 feet. The shorter side of the closet is 9/2 feet. What is the area of the closet in square feet?

(A) 37

(B) 27

(C) 54/4

(D) 21/4

(E) 5

A rectangle is divided by its diagonal into two congruent right triangles.

Rule: If a right triangle has a leg:hypotenuse ratio of 3:5 (or 4:5, or legs in ratio 3:4), it is a 3-4-5 right triangle.

Common 3x-4x-5x triangles include 6-8-10 (x=2), 9-12-15 (x=3), 12-16-20 (x=4), etc.

The short leg of this right triangle in the closet is $$\frac{9}{2}$$ feet. The hypotenuse is $$\frac{15}{2}$$ feet.

Focus on the numerator. Without any calculation we can say the other leg must be $$\frac{12}{2}$$ feet long. The numerator matches the 9-12-15 pattern.
Keep the same denominator. OR

$$(leg1)^2 + (leg2)^2 = h^2$$
$$\frac{9}{2}^2 + (leg2)^2 = \frac{15}{2}^2$$
$$(leg2)^2 = (\frac{225}{4}-\frac{81}{4})$$
$$\sqrt{(leg2)^2}=\sqrt{\frac{144}{4}}=\frac{12}{2} = 6$$

Area $$= L*W = \frac{9}{2}*6=\frac{54}{2}=27$$

*The multiplier is $$\frac{3}{2}$$.$$(3*\frac{3}{2})=\frac{9}{2}$$, and $$(5*\frac{3}{2})=\frac{15}{2}$$. If you focus on the numerator and just make the second leg's denominator match the denominator of the other two lengths, you do not need to find the multiplier or use the Pythagorean theorem.
Intern
Joined: 05 Dec 2017
Posts: 5
Re: The diagonal of the floor of a rectangular closet is 15/2 feet. The sh  [#permalink]

### Show Tags

07 Mar 2018, 09:04
Hey Bunuel is the qustion asking to calculate the area of the closet or the rectangular floor?
Math Expert
Joined: 02 Sep 2009
Posts: 51035
Re: The diagonal of the floor of a rectangular closet is 15/2 feet. The sh  [#permalink]

### Show Tags

07 Mar 2018, 09:17
Salamander911 wrote:
Hey Bunuel is the qustion asking to calculate the area of the closet or the rectangular floor?

I think the solutions above answer your question.
_________________
Re: The diagonal of the floor of a rectangular closet is 15/2 feet. The sh &nbs [#permalink] 07 Mar 2018, 09:17
Display posts from previous: Sort by

# The diagonal of the floor of a rectangular closet is 15/2 feet. The sh

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.