Answer: The length of the diagonal of the square is 7.07 inches.
Step-by-step explanation: We are given to find the length of the diagonal of a square whose side is of measure 5 in.
As shown in the attached figure below, ABCD is a square, where
AB = BC = CD = DA = 5 in. and AC is one of the diagonals.
Since all the four angles of a square are right-angles, so triangle ABC will be a right-angled at angle ABC.
So, the diagonal AC is the hypotenuse of the triangle.
Applying the Pythagoras theorem in the right-angled triangle ABC, we have
[tex]AC^2=AB^2+BC^2\\\\\Rightarrow AC=\sqrt{5^2+5^2}\\\\\Rightarrow AC=\sqrt{25+25}\\\\\Rightarrow AC=\sqrt{50}\\\\\Rightarrow AC=5\sqrt2\\\\\Rightarrow AC=5\times 1.4142\\\\\Rightarrow AC=7.07.[/tex]
Thus, the length of the diagonal of the square is 7.07 inches.
