NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 16:47 It is currently 25 Apr 2024, 16:47
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

In right triangle HEK, HK is the hypotenuse. If HK is 10√2 and EH + EK

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619025 [2]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
In right triangle HEK, HK is the hypotenuse. If HK is 10√2 and EH + EK [#permalink] New post   20 Dec 2019, 03:10
2
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

25% (medium)

Question Stats:

81% (01:47) correct 19% (02:43) wrong based on 69 sessions
Hide Show timer Statistics
In right triangle HEK, HK is the hypotenuse. If HK is 10√2 and EH + EK = 20, what is the area of the triangle HEK?

A. 50
B. 75
C. 25√2
D. 100
E. 50√2
ShowHide Answer
Official Answer
A
User avatar
L
rajatchopra1994
VP
VP
Joined: 16 Feb 2015
Posts: 1080
Own Kudos [?]: 1025 [0]
Given Kudos: 30
Location: United States
Send PM
Re: In right triangle HEK, HK is the hypotenuse. If HK is 10√2 and EH + EK [#permalink] New post   20 Dec 2019, 03:24
Bunuel wrote:
In right triangle HEK, HK is the hypotenuse. If HK is 10√2 and EH + EK = 20, what is the area of the triangle HEK?

A. 50
B. 75
C. 25√2
D. 100
E. 50√2


Explanation:
let EH=X
EK=20-X
x^2 + (20-x)^2 = (10√2)^2
x^2+400+x^2-40x = 200
2x^2 -40x +200 =0
x^2 - 20x +100
(x-10)(x-10)=0
x=10

So EH=EK= 10

Area= 10*10*1/2
=50

IMO-A
User avatar
L
TheNightKing
VP
VP
Joined: 18 Dec 2017
Posts: 1170
Own Kudos [?]: 991 [0]
Given Kudos: 421
Location: United States (KS)
GMAT 1: 600 Q46 V27
Send PM
Re: In right triangle HEK, HK is the hypotenuse. If HK is 10√2 and EH + EK [#permalink] New post   27 Jan 2020, 18:04
Bunuel wrote:
In right triangle HEK, HK is the hypotenuse. If HK is 10√2 and EH + EK = 20, what is the area of the triangle HEK?

A. 50
B. 75
C. 25√2
D. 100
E. 50√2



Well, you can either solve as per the explanation above.

Or

Realize 45-45-90 triangle has ratio of sides as 1:1:root 2. And just try that. 10root2 gives us the hint that other sides can be 10 each.

Works well. :)
User avatar
P
MHIKER
Director
Director
Joined: 14 Jul 2010
Status:No dream is too large, no dreamer is too small
Posts: 972
Own Kudos [?]: 4928 [0]
Given Kudos: 690
Concentration: Accounting
Send PM
Re: In right triangle HEK, HK is the hypotenuse. If HK is 10√2 and EH + EK [#permalink] New post   08 Jan 2021, 13:26
Top Contributor
Bunuel wrote:
In right triangle HEK, HK is the hypotenuse. If HK is 10√2 and EH + EK = 20, what is the area of the triangle HEK?

A. 50
B. 75
C. 25√2
D. 100
E. 50√2


HEK is a right triangle. Hypotenuse HK=10√2, which reminded us of the properties of 45°, 45°, and 90°, where the hypotenuse is √2 of either side of the triangle. Thus each side is 10 (base and leg)

The area is \(\frac{1}{2}*10*10=50\)

The answer is \(A\).
GMAT Club Bot
gmatclubot
Re: In right triangle HEK, HK is the hypotenuse. If HK is 10√2 and EH + EK [#permalink]
08 Jan 2021, 13:26
Moderators:
Bunuel
Math Expert
92915 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions