Answer:
8.5
Step-by-step explanation:
The Pythagorean theorem (a^2 + b^2 = c^2) can be used to solve this problem. We have a square with a side length of 6 inches. That means all of the sides will be 6 inches. That also means the base and the height are 6 inches. Let's now cut the square in half diagonally. We have a slope now, which is the hypotenuse. Let's put these values in the Pythagorean theorem and solve for the diagonal, or the hypotenuse:
[tex]6^{2} +6^{2} = c^{2}[/tex]
This is equivalent to:
[tex]36 + 36 = c^{2}[/tex]
[tex]\sqrt{72} =\sqrt{c^{2} }[/tex]
C = 8.5 (rounded)
The length of the diagonal in inches should be [tex]6\sqrt 2[/tex] inches
Since a square has a side length of 6 inches.
So here we assume c be the diagonal
And, a and b be the square sides
So,
[tex]c^2 = a^2 + b^2\\\\c = \sqrt (a^2 + b^2)\\\\c = \sqrt (6^2 + 6^2)\\\\c = \sqrt 72\\\\c = \sqrt (36 \times 2)\\\\c = 6\sqrt 2\\\\[/tex]
Therefore, The length of the diagonal in inches should be [tex]6\sqrt 2[/tex] inches
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