A square has diagonal length 9 m. What is the side length of the square to the nearest centimeter?

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Answer 1 · 2018-02-26T18:42:48

see a solution process below:

By definition a square is a flat object with 4 equal sides and 4 right angles. Therefore, we can use the Pythagorean Theorem to solve this problem.

The Pythagorean Theorem states:

#a^2 + b^2 = c^2# Where

#a# and #b# are the legs of the triangle.

#c# is the hypotenuse of the triangle. In this problem the diagonal is the hypotenuse and we are told it is #9"m"#

Also, because this is a square, the two legs of the right triangle are of equal length so we can call them #s# and rewrite the formula as:

#s^2 + s^2 = (9"m")^2#

#2s^2 = 81"m"^2#

We can now solve for #s#:

#sqrt(2s^2) = sqrt(81"m"^2)#

#sqrt(2)sqrt(s^2) = 9"m"#

#sqrt(2)s = 9"m"#

#(sqrt(2)s)/color(red)(sqrt(2)) = (9"m")/color(red)(sqrt(2))#

#(color(red)(cancel(color(black)(sqrt(2))))s)/cancel(color(red)(sqrt(2))) = (9"m")/1.414213562373095#

#s = 6.363961030678928"m"#

Or

#s = 6.36"m"# rounded to the nearest centimeter