Last visit was: 29 May 2026, 07:30 It is currently 29 May 2026, 07:30
Home
Messages
MBA Fair
Tests
Schools
Events
Close
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
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
805+ (Hard)|   Geometry|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 29 May 2026
Posts: 110,897
Own Kudos:
817,733
Given Kudos: 106,508
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 110,897
Kudos: 817,733
The figure shows a window that is in the shape of a rectangle with 16 Nov 2022, 11:48
Kudos
Add Kudos
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

33% (03:18) correct 67% (02:29) wrong based on 24 sessions

History

Date
Time
Result
Not Attempted Yet

The figure shows a window that is in the shape of a rectangle with a semicircle at the top. The radius of the semicircle is x feet, and the perimeter of the window is 26 feet. What is the total area, in square feet, of the window in terms of x?

A. \(13x-(π+2)x^2\)

B. \(26x-2x^2\)

C. \(26x-(\frac{π}{2}+2)x^2\)

D. \(26x-(\frac{π}{2}+4)x^2\)

E. \(26x-(\frac{3π}{2}+2)x^2\)

Show Spoiler
Attachment:
Untitled.png
Untitled.png [ 7.14 KiB | Viewed 2437 times ]
ShowHide Answer
Official Answer
C
User avatar
divyadna
User avatar
Joined: 21 Dec 2021
Last visit: 30 Jan 2024
Posts: 311
Own Kudos:
331
Given Kudos: 242
Posts: 311
Kudos: 331
The figure shows a window that is in the shape of a rectangle with Updated on: 17 Nov 2022, 02:30
Originally posted by divyadna on 16 Nov 2022, 12:43.
Last edited by divyadna on 17 Nov 2022, 02:30, edited 2 times in total.
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Posted from my mobile device
Attachments

File comment: Answer is option D
IMG_20221117_010959__01__01.jpg
IMG_20221117_010959__01__01.jpg [ 1.91 MiB | Viewed 2292 times ]

User avatar
truplayer257
User avatar
Joined: 19 Jan 2017
Last visit: 06 May 2025
Posts: 27
Own Kudos:
28
 [1]
Given Kudos: 5
Posts: 27
Kudos: 28
 [1]
The figure shows a window that is in the shape of a rectangle with 16 Nov 2022, 18:09
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
You made a mistake, you’re including “2x” twice when it should only be included once. After doing this, you should get option C, which is the correct choice.

Posted from my mobile device
User avatar
dsp9846
User avatar
Joined: 31 Jan 2022
Last visit: 24 Jul 2024
Posts: 18
Own Kudos:
33
 [1]
Given Kudos: 15
Posts: 18
Kudos: 33
 [1]
The figure shows a window that is in the shape of a rectangle with 16 Nov 2022, 20:36
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Let's say the length of the window is y,

The radius of the semicircle is x that is given.

now based on that perimeter of the window = 2x+2y+(2πx)/2 = 2x + 2y + πx

now perimeter is given 26 feet,

so, 2x + 2y + πx = 26

2y = 26 - 2x - πx

Now the area of the window = area of the rectangle portion + area of the semicircle
= (y)(2x) + (πx^2)/2
= (x)(2y) + (πx^2)/2
= (x)(26 - 2x - πx) + (πx^2)/2
= 26x - 2x^2 - πx^2 + (πx^2)/2
= 26x - 2x^2 - (πx^2)/2
= 26x−(π/2+2)x^2

So answer is option C
User avatar
SaquibHGMATWhiz
User avatar
GMATWhiz Representative
Joined: 23 May 2022
Last visit: 12 Jun 2024
Posts: 623
Own Kudos:
781
 [1]
Given Kudos: 6
Location: India
GMAT 1: 760 Q51 V40
Expert
Expert reply
GMAT 1: 760 Q51 V40
Posts: 623
Kudos: 781
 [1]
The figure shows a window that is in the shape of a rectangle with 17 Nov 2022, 04:47
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

The figure shows a window that is in the shape of a rectangle with a semicircle at the top. The radius of the semicircle is x feet, and the perimeter of the window is 26 feet. What is the total area, in square feet, of the window in terms of x?

A. \(13x-(π+2)x^2\)

B. \(26x-2x^2\)

C. \(26x-(\frac{π}{2}+2)x^2\)

D. \(26x-(\frac{π}{2}+4)x^2\)

E. \(26x-(\frac{3π}{2}+2)x^2\)

Show Spoiler
Attachment:
Untitled.png
Show more

Solution:

  • Let us assume the length of the rectangle be \(l\)
  • Perimeter of the window = perimeter of the dome + 3 sides of rectangle
    \(⇒26=\pi x+l+l+2x\)
    \(⇒26=\pi x+2l+2x\)
    \(⇒2l=26-\pi x-2x\)
    \(⇒l=13-\frac{\pi x}{2}-x\)
  • Area of the window = area of dome + area of rectangle
    \(=\frac{\pi x^2}{2}+2lx\)
    \(=\frac{\pi x^2}{2}+2(13-\frac{\pi x}{2}-x)x\)
    \(=\frac{\pi x^2}{2}+26-\pi x^2-2x^2\)
    \(=26-\frac{\pi x^2}{2}-2x^2\)
    \(=26-x^2(\frac{\pi}{2}+2)\)

Hence the right answer is Option C
Moderator:
Bunuel
Math Expert
110897 posts