Problem Solving

A square is inscribed in a semicircle of radius 1. The area of the square is
(a) 4/5
(b) 3/4
(c) 3pi/4
d) 4pi/5
e) 1/2

dtweah wrote:A square is inscribed in a semicircle of radius 1. The area of the square is
(a) 4/5
(b) 3/4
(c) 3pi/4
d) 4pi/5
e) 1/2

Hi dtweah,

My answer is A.

Please let me know if I am correct. If yes, I can post my explanation.

Pranay

Pranay,

Pls post yr explanation - I eyeballed the question and picked A too, but don't know a way to solve it.

Thanks

Bhattu wrote:Pranay,

Pls post yr explanation - I eyeballed the question and picked A too, but don't know a way to solve it.

Thanks

Hi Bhattu,

Please refer the diagram in the attached file,

OA=OB=1 since radius of circle is 1, given

Assume the length of side of square is l => Area is l^2

and an right angled triangle is formed between points A, O and the point intersection of the line extended from centre O to chord AB,

length of the extended line is l,
Now, try to find out the value l from,

l^2 + (l/2)^2 = 1

=> l^2 = 4/5.

Thus, A.

Please bear with the diagram as I could not find any other tool to draw a diagram better than this.

Pranay