I think the image is a bit too small... Let me write the question down...
The perimeter of a certain isosceles right triangle is 16 + 16*sqrt(2). What is the length of the hypotenuse of the triangle?
(a) 8
(b) 16
(c) 4*sqrt(2)
(d) 8*sqrt(2)
(e) 16*sqrt(2)
BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course
Redeem
Featured Course
Target Test Prep GMAT OnDemand
Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.
- 715+ score guarantee — highest in the industry (99th percentile)
- 52 chapters · 1,500+ lessons · 4,000+ practice questions
- 400 hours of video · 1,500+ instructor-led HD smartboard lessons
- 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
- 24/7 live support + weekly Zoom office hours with GMAT instructors
- TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
- 1,200+ flashcards + AI-powered study assistant & daily calendar
- OnDemand, LiveTeach & GMAT Bootcamp formats available
- Also: GRE, SAT Math & Executive Assessment courses
- MBA Admissions Consulting now available
- 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
- 200,000+ students served
- 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★
5.0
(559 reviews)
130-pt guarantee
$0 to start
then $127/mo
Triangle/Isoceles
Source: Beat The GMAT — Problem Solving |
The question tells you that it is an isoceles right triangle. In an isoceles triangle, 2 sides are equal. Thus, we can deduce that this is a 45-45-90 triangle.
Labeling the triangle, one side is x, the other side is also x, the hypotenuse is x(square root)2. Based on properties of 45-45-90 triangles.
THe question tells you that the perimeter is equal to 16+16(square root)2. Set that equal to how you labeled the figure. So x+x+x(square root)2 = 16+16(square root)2.
From here you can see that the value is 16.
Labeling the triangle, one side is x, the other side is also x, the hypotenuse is x(square root)2. Based on properties of 45-45-90 triangles.
THe question tells you that the perimeter is equal to 16+16(square root)2. Set that equal to how you labeled the figure. So x+x+x(square root)2 = 16+16(square root)2.
From here you can see that the value is 16.
Thanks for your reply...
I did the same approach when doing this problem, x + x + x*sqrt(2) = 16 + 16*sqrt(2). But how do you deduce the hypotenuse = 16 just from the algebra shown above? I'm still not following the logic...
Can anyone help?
I did the same approach when doing this problem, x + x + x*sqrt(2) = 16 + 16*sqrt(2). But how do you deduce the hypotenuse = 16 just from the algebra shown above? I'm still not following the logic...
Can anyone help?
-
abhimanyu.tanwar
- Senior | Next Rank: 100 Posts
- Posts: 55
- Location: Pune, India
- Thanked: 1 times
since the perimeter is 16 + 16*(sqrt)2 and the triangle is isosceles we can say that either the hypotenuse is 16 or 16*(sqrt)2.
let us assume it is 16(sqrt)2 ... hence the other two sides should be 16/2 each .. which gives us 8.
as it is a right angle triangle, we can apply pythagoras theorem here .. which gives us the hypotenuse as 8(sqrt)2 ... which contradicts with the value of hypotenuse (16(sqrt)2) we already assumed in the beginning .. hence hypotenuse can't be 16(sqrt)2
apply the same method by taking hypotenuse as 16 and the other two sides as 8(sqrt)2 . this will provide the desired result.
Hope it helps
let us assume it is 16(sqrt)2 ... hence the other two sides should be 16/2 each .. which gives us 8.
as it is a right angle triangle, we can apply pythagoras theorem here .. which gives us the hypotenuse as 8(sqrt)2 ... which contradicts with the value of hypotenuse (16(sqrt)2) we already assumed in the beginning .. hence hypotenuse can't be 16(sqrt)2
apply the same method by taking hypotenuse as 16 and the other two sides as 8(sqrt)2 . this will provide the desired result.
Hope it helps
Regards
Abhimanyu
Abhimanyu
-
GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Location: New York, NY
- Thanked: 13060 times
- GMAT Score:790
The perimeter of a certain isosceles right triangle is 16 +16√2. What is the length of the hypotenuse of the triangle?
A. 8
B. 16
C. 4√2
D. 8√2
E. 16√2
In an isosceles right triangle, the sides are proportioned s:s:s√2 so that h = s√2. Let's plug in the answer choices, which represent the length of h (the hypotenuse):
Answer choice C:
4√2 = s√2
s = 4
p = s+s+h = 4+4+4√2 = 8+4√2. Doesn't work.
Answer choice B:
16 = s√2
s = 16/√2 = (16√2)/√2*√2) = (16√2)/2 = 8√2
p = s+s+h = 8√2 + 8√2 + 16 = 16√2 + 16. Success!
The correct answer is B.
A. 8
B. 16
C. 4√2
D. 8√2
E. 16√2
In an isosceles right triangle, the sides are proportioned s:s:s√2 so that h = s√2. Let's plug in the answer choices, which represent the length of h (the hypotenuse):
Answer choice C:
4√2 = s√2
s = 4
p = s+s+h = 4+4+4√2 = 8+4√2. Doesn't work.
Answer choice B:
16 = s√2
s = 16/√2 = (16√2)/√2*√2) = (16√2)/2 = 8√2
p = s+s+h = 8√2 + 8√2 + 16 = 16√2 + 16. Success!
The correct answer is B.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
