The question is A square and an equilateral triangle have equal perimeters. The area of the triangle is 2√3 sq<span>uare inches. What is the number of inches in the length of the diagonal of the square? </span> we know that the area of an equilateral triangle is applying the law of sines A=(1/2)*b²*sin 60°-----> 2√3=(1/2)*b²*√3/2 (2√3)*(2/√3)=(1/2)*b² 4=(1/2)*b² b²=8 b=√8 in
perimeter of the triangle=3*b-----> 3*√8 in
let x----> the length side of the square perimeter of the square=perimeter of the triangle perimeter of the square=3*√8 in and perimeter of the square=4*x 4*x=3*√8 x=(3/4)*√8----> x=(3/2)*√2 in
find the diagonal of the square applying the Pythagoras theorem D²=x²+x²----> D²=2*x²----> D²=2*((3/2)*√2)² D²=2*(9/4)*2 D²=9 D=3 in
the answer is the number of inches in the length of the diagonal of the square is 3
