The diagonal of a square has length #12sqrt2# ft. How do you find the length of the side of the square?

1 Answer
Mar 9, 2018

Answer:

length of side: #12# feet

Explanation:

Since the figure is a square, it's sides have the same length; Lets call this length #s#

The diagonal forms a hypotenuse, #h#, with two of the sides
and, based on the Pythagorean Theorem,
#color(white)("XXX")s^2+s^2=h^2#
and since the diagonal (#h#) is given as having a length of #12sqrt(2)#,
we have
#color(white)("XXX")2s^2=(12sqrt(2))^2=12^2 * (sqrt(2))^2= 12^2 * 2#

#color(white)("XXX")rarr s^2=12^2#

and since (in the normal world) lengths can not be negative:
#color(white)("XXX")s=12#

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An easier way to see this is to remember the standard right triangle (often used in trigonometry):
enter image source here
and realize the given triangle is a similar triangle simply scaled up by a factor of #12#