Source: Revised GRE PDF 1st Ed. Section 5: Math; #1 (p. 71)


Two right triangles, sides 4 4 and 4 8

Column A: x; Column B: y

3 Explanations


Eliza J Davidson

I tried solving this question using the Pythagorean theorem, and got the question incorrect. Can you please demonstrate how to solve it that way?


Oct 13, 2017 • Comment

Jonathan , Magoosh Tutor

Hi Eliza,
The Pythagorean Theorem should work! Let's look:
For one triangle you get:
8^2 - 4^2 = x^2 ---> x^2 = 48
For the other you get
4^2 + 4^2 = y^2 ---> y^2 = 32

So x^2 > y^2 so x must be greater than y.

You should know the 30-60-90 and 45-45-90 triangles ratios too, though :)

Nov 6, 2017 • Reply


Yilan Shi

you know all legs of right triangls are SHORTER than hypothenus. But the hypothenus of another triangle may be shorter than the leg of triangle #2.

That hypothetnus is longer than a leg of a right triangle, ONLY applies when you're talkign about th same tiangle.

Sep 25, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

Hi Yilan :)

Happy to clarify! You're correct that when we say the hypotenuse is the longest side of a triangle, we are only referring to the three sides of one specific triangle. That's the case here, as we're able to show that x, one of the legs of the first triangle, has a greater length than y, the hypotenuse of the second triangle:

x = 4sqrt(3)
y = 4sqrt(2)


I hope this helps!

Sep 26, 2016 • Reply


Gravatar Chris Lele, Magoosh Tutor

Oct 3, 2012 • Comment

Add Your Explanation

You must have a Magoosh account in order to leave an explanation.

Learn More About Magoosh