It is currently 13 Dec 2018, 17:32

### 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

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

# If a right triangle has legs

Author Message
TAGS:
Moderator
Joined: 18 Apr 2015
Posts: 5166
Followers: 77

Kudos [?]: 1033 [0], given: 4655

If a right triangle has legs [#permalink]  14 Nov 2017, 08:12
Expert's post
00:00

Question Stats:

85% (00:44) correct 14% (00:00) wrong based on 14 sessions

If a right triangle has legs of 20 cm and 21 cm, what is the length of the hypotenuse?

A. $$\sqrt{41}$$ cm

B. 20.5 cm

C. 29 cm

D 41 cm

E. 45 cm
[Reveal] Spoiler: OA

_________________
GRE Instructor
Joined: 10 Apr 2015
Posts: 1238
Followers: 46

Kudos [?]: 1123 [2] , given: 7

Re: If a right triangle has legs [#permalink]  14 Nov 2017, 08:51
2
KUDOS
Expert's post
Carcass wrote:

If a right triangle has legs of 20 cm and 21 cm, what is the length of the hypotenuse?

A. $$\sqrt{41}$$ cm

B. 20.5 cm

C. 29 cm

D 41 cm

E. 45 cm

[Reveal] Spoiler: OA
OA in 24 hours, kudo for the right solution/explanation

The Pythagorean Theorem says: (leg)² + (other leg)² = (hypotenuse)²

We get: (20)² + (21)² = (hypotenuse)²
Evaluate: 400 + 441 = (hypotenuse)²
Evaluate: 841 = (hypotenuse)²
So, hypotenuse = √841 = 29

[Reveal] Spoiler:
C

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

PrepScholar Expert
Joined: 07 Nov 2017
Posts: 14
WE: Education (Education)
Followers: 1

Kudos [?]: 18 [2] , given: 0

Re: If a right triangle has legs [#permalink]  14 Nov 2017, 09:04
2
KUDOS
Here are three easy steps for answering any quant question on the GRE!

First, Survey the Question. Here you'll want to identify what skill is likely being tested. That will help you narrow down what kind of information you'll need to solve the question. Pay attention to mathy sounding words. Doing so here, the words "triangle" and "hypotenuse" and clues that we'll use either the Pythagorean Theorem or Pythagorean Triples.

Second, Develop a Plan. It's important that your plan takes place on your paper. Otherwise you'll waste time going 2 steps forward and 1 step backward (and even 2 steps backward sometimes!). We know that we want to use the Pythagorean Theorem, so let's write that down on our paper.

$$c^{2} = a^{2} + b^{2}$$

So the plan is shaping up here. We know that a=20 and b=21, so let's plan to plug in the numbers and finish this question!

Third, Solve the Question. Plugging in a and b into our equation we get:

$$c^{2} = 20^{2} + 21^{2}$$

$$c^{2} = 400 + 441$$

$$c^{2} = 841$$

So for c, we need the square root of 841. Now instead of trying to solve for it, let's estimate it instead. Think of a number close to 841 where you know it's square root. A good number here would be 900, as we know that the square root of 900 is 30. So the square root of 841 should be slightly less than 30. Looking at our answer choices, that eliminates D and E. A is way too small. B, 20.5, is less than one of our legs, and we know that the hypotenuse of a right triangle MUST be the longest side. So we're left with C as the only answer remaining. And we didn't even need to calculate the square root of 841!
_________________

Corey
PrepScholar GRE Instructor

https://gre.prepscholar.com

Come attend a free GRE Workshop: Complete Mastery of GRE Quantitative Comparison. Sign up today while spots are still open!
https://events.genndi.com/channel/GRE-Workshop

Re: If a right triangle has legs   [#permalink] 14 Nov 2017, 09:04
Display posts from previous: Sort by