How do you use the Pythagorean theorem to find the length of the diagonal of a square that has an area of 100 square inches?

1 Answer
CW
Feb 25, 2017

#10sqrt2#

Explanation:

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As shown in the diagram, #ABCD# is a square, #AC# is the a diagonal, and #s# is the side length.

Area of a square #A_s= s^2#
Given #A_s=100, => s=sqrt100=10#

Diagonal #AC# divides the square #ABCD# into two congruent isosceles right triangles, #DeltaABC and DeltaADC#. The diagonal #AC# is the hypotenuse of #DeltaABC and DeltaADC#.

By Pythagorean Theorem, we know that :
#AC^2=AB^2+BC^2=s^2+s^2#
#=> AC^2=2s^2#
#=> AC=sqrt(2s^2)=s*sqrt2=10sqrt2#

Foot note: A square has two diagonals, in this case, #AC and BD#. #AC and BD# are congruent, #=> AC=BD#.

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