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23 Jun 2020, 03:09
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C
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28% (02:30) correct
72%
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wrong
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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
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2020-06-23_1402.png [ 31.55 KiB | Viewed 5426 times ]
24 Jun 2020, 03:37
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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
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General Discussion
23 Jun 2020, 05:06
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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
