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RenB
Joined: 13 Jul 2022
Last visit: 02 Mar 2026
Posts: 388
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Location: India
Concentration: Finance, Nonprofit
Schools: Stanford '26 Wharton '26 (D) Booth '26 (D) Yale '26 (D) CBS '26 (A$$$) Darden '26 (WL) HBS '26 (D) Ross '26 (A$$$$) LBS '26 (D) Tuck '26 (A$$) Kellogg '26 (A)
GMAT Focus 1: 715 Q90 V84 DI82 
GPA: 3.74
WE:Corporate Finance (Consulting)
Schools: Stanford '26 Wharton '26 (D) Booth '26 (D) Yale '26 (D) CBS '26 (A$$$) Darden '26 (WL) HBS '26 (D) Ross '26 (A$$$$) LBS '26 (D) Tuck '26 (A$$) Kellogg '26 (A)
GMAT Focus 1: 715 Q90 V84 DI82
Posts: 388
01 Oct 2023, 05:33
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
52% (01:52) correct
48%
(02:05)
wrong
based on 66
sessions
History
Date
Time
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Not Attempted Yet
PQR is an isosceles right-angled triangle with perimeter 8 + 8√2 and longest side PR. What is the length of side PR?
A. 4
B. 8
C. \(4\sqrt{2}\)
D. \(8\sqrt{2}\)
E. 16
A. 4
B. 8
C. \(4\sqrt{2}\)
D. \(8\sqrt{2}\)
E. 16
01 Oct 2023, 08:52
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RenB
The given triangle is a 45 - 45 - 90 triangle. Hence, the sides of the triangle are in the ratio \(1:1:\sqrt{2}\)
Attachment:
Screenshot 2023-10-01 211605.png [ 28.34 KiB | Viewed 1033 times ]
Given:
\(2x + \sqrt{2}x = 8 + 8\sqrt{2}\)
\(x(2 + \sqrt{2}) = 8(1 + \sqrt{2})\)
\(x = 8\frac{(1 + \sqrt{2})}{(2 + \sqrt{2})}\)
\(x = 8\frac{(1 + \sqrt{2})(2 - \sqrt{2})}{(2 + \sqrt{2})(2 - \sqrt{2})}\)
\(x = 4\sqrt{2}\)
PR = \(x\sqrt{2} = 4\sqrt{2} * \sqrt{2} = 8\)
Option B
mialanknox
Joined: 15 May 2019
Last visit: 19 Oct 2025
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Location: Switzerland
Concentration: Finance, General Management
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WE:Investment Banking (Finance: Investment Banking)
01 Oct 2023, 10:45
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RenB
Perimeter = 8 + 8√2
We know triangle is an isosceles triangle
...that means two sides are equal
...so the two equal sides are either 4+4=8 or 4√2+4√2=8√2
...we know that the sum of longer side must be less than the sum of two sides and greater than the difference of two sides
...that means hypotenuse is <8 or <8√2
...if we assume two sides are 4 and 4
then 8√2 = 8 × 1.4 = 11.2 which is greater than sum of two sides (8) so the two sides are not equal to 4 each.
...if we assume two sides are equal to 8√2 = 11.4 then the longer side can be 8 because it is less than the sum of two sides.
Therefore, option B is the answer.
Time to solve: 30 seconds
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