BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
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
Start Free 5-Day Trial Read 559 Reviews →

Diagonal of a cube

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Legendary Member
Posts: 566
Joined: Fri Jan 04, 2008 11:01 am
Location: Philadelphia
Thanked: 31 times
GMAT Score:640
by AleksandrM » Wed Jun 11, 2008 9:27 am
The diagonal of a cube of side x is xsqroot3.

This can be found by applying the Pythagorean Theorem twice (first to find the diagonal of a face of the cube, xsqroot2, and then to find the diagonal through the center, xsqroot3).

Can someone please demonstrate for me the latter part (xsqroot3).

Assume we are dealing with a cube with side 4.

Thanks.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 566
Joined: Fri Jan 04, 2008 11:01 am
Location: Philadelphia
Thanked: 31 times
GMAT Score:640

by AleksandrM » Wed Jun 11, 2008 9:31 am
Never mind I got it. Just imagine a cube that has been cut through the side

You have base 4 and hight 4sqroot2:

(4sqroot2)^2 + 4^2 = x^2 diagonal from one end of cube to ther other

x = 4sqroot3
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 178
Joined: Wed May 14, 2008 3:51 pmFollowed by: 1 member
Thanked: 16 times
GMAT Score:99%+

by egybs » Wed Jun 11, 2008 9:46 am
Diag1 = Diagonal of one side of the cube
Diag2 = Diagonal of the entire cube


Diag1^2 = x^2+x^2
Diag1 = (2x^2)^.5 = x(2^.5)
Diag2^2 = (x(2^.5))^2 + x^2
Diag2^2 = 2x^2 + x^2 = 3x^2
Diag2 = (3x^2)^.5 = x(3^.5)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2623
Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members
Location: Montreal
Thanked: 1090 times
GMAT Score:780

by Ian Stewart » Wed Jun 11, 2008 12:09 pm
You could also use the three-dimensional version of the Pythagorean Theorem:

d^2 = x^2 + y^2 + z^2

where d is the diagonal inside a box ('rectangular prism', in math terms) of dimensions x by y by z.

Thus in the special case of a cube measuring x by x by x,

d^2 = x^2 + x^2 + x^2
d^2 = 3x^2
d = root(3)*x

This won't be useful very often on the GMAT, but occasionally it does help.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 178
Joined: Wed May 14, 2008 3:51 pmFollowed by: 1 member
Thanked: 16 times
GMAT Score:99%+

by egybs » Wed Jun 11, 2008 12:24 pm
Heh good point Ian... that's a lot nicer!

Ian Stewart wrote:You could also use the three-dimensional version of the Pythagorean Theorem:

d^2 = x^2 + y^2 + z^2

where d is the diagonal inside a box ('rectangular prism', in math terms) of dimensions x by y by z.

Thus in the special case of a cube measuring x by x by x,

d^2 = x^2 + x^2 + x^2
d^2 = 3x^2
d = root(3)*x

This won't be useful very often on the GMAT, but occasionally it does help.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1