The diagonal of a square is 26 inches, what is the length of the side and the perimeter of the square?

1 Answer
Jim G.
Dec 18, 2017

#13sqrt2" and "52sqrt2#

Explanation:

#"the diagonal of the square 'splits' the square into"#
#"2 congruent right triangles"#

#"consider the right triangle"#

#"with hypotenuse "=26" and legs "=x#

#"using "color(blue)"Pythagoras' theorem"#

#rArrx^2+x^2=26^2#

#rArr2x^2=676#

#rArrx^2=676/2=338#

#rArrx=sqrt338=13sqrt2#

#rArr"length of side "=13sqrt2larrcolor(blue)"exact value"#

#"and perimeter "=4xx13sqrt2=52sqrt2larrcolor(blue)"exact value"#

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