Let A B C be an equilateral triangle with side length 10. A square P Q R S is inscribed in it, with P on A B , Q, R on B C and S on A C . If the area of the square P Q R S is m+n k where m, n are integers and k is a prime number then determ

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Let A B C be an equilateral triangle with side length 10. A square P Q R S is inscribed in it, with P on A B , Q, R on B C and S on A C . If the area of the square P Q R S is m+n k where m, n are integers and k is a prime number then determine the value of m+n k^2

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Correct answer: 10

aligned & a+2 x=10 & also 60^ = a x & x= a 3 & a= 10 3 2+ 3 & Area of square =a^2=300(7-4 3 ) & m=2100, n=-1200, k=3 & m+n k^2 = 900 9 =10 aligned

Let A B C be an equilateral triangle with side length 10. A square P Q R S is inscribed in it, with P on A B , Q, R on B C and S on A C . If the area of the square P Q R S is m+n k where m, n are integers and k is a prime number then determine the value of m+n k^2

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