|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
23 Jun 2020, 03:09
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
28% (02:30) correct
72%
(01:50)
wrong
based on 88
sessions
History
Date
Time
Result
Not Attempted Yet
Two side-by-side squares are inscribed in a semicircle as shown above. If the semicircle has a radius of 10, what is the total area of the two squares?
A. 80
B. 90
C. 100
D. 120
E. Cannot be determied
Are You Up For the Challenge: 700 Level Questions
Attachment:
2020-06-23_1402.png [ 31.55 KiB | Viewed 5829 times ]
24 Jun 2020, 03:37
Kudos
Bookmarks
Side or larger square = a, side of smaller square = b, OX = c
r^2 = a^2 + (a-c)^2
r^2 = b^2 + (b+c)^2
=> a^2 + (a-c)^2 = b^2 + (b+c)^2
=> 2*a^2 - 2ac = 2*b^2 + 2bc
=> a^2 - b^2 = c(a+b)
=> a-b = c
Substitute in any equation, r^2 = a^2 + (a-(a-b))^2 = a^2 + b^2 => a^2 + b^2 = 100
or,
we can obtain the result in a generalized manner. since no specific ratio has been given with respect to the sides of the squares, let's consider them to be of equal size.
So the common side will be perpendicular at origin.
Let side of each square be x.
r^2 = x^2 + x^2 = 2*x^2
2*x^2 is nothing but the combined area of the squares, which is equal to 100.
Ans: C
r^2 = a^2 + (a-c)^2
r^2 = b^2 + (b+c)^2
=> a^2 + (a-c)^2 = b^2 + (b+c)^2
=> 2*a^2 - 2ac = 2*b^2 + 2bc
=> a^2 - b^2 = c(a+b)
=> a-b = c
Substitute in any equation, r^2 = a^2 + (a-(a-b))^2 = a^2 + b^2 => a^2 + b^2 = 100
or,
we can obtain the result in a generalized manner. since no specific ratio has been given with respect to the sides of the squares, let's consider them to be of equal size.
So the common side will be perpendicular at origin.
Let side of each square be x.
r^2 = x^2 + x^2 = 2*x^2
2*x^2 is nothing but the combined area of the squares, which is equal to 100.
Ans: C
Attachments
Untitled.png [ 39.15 KiB | Viewed 5350 times ]
General Discussion
23 Jun 2020, 05:06
Kudos
Bookmarks
Explanation;
let small Square with side X
Large Square with side Y
By using Pythagoras theorem we can deduce to below formula
Area : X^2 + Y^2 = R^2
100
IMO-C
let small Square with side X
Large Square with side Y
By using Pythagoras theorem we can deduce to below formula
Area : X^2 + Y^2 = R^2
100
IMO-C
