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

Question

Nathan Axel · Accepted Answer

length of side: #12# feet

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#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

An easier way to see this is to remember the standard right triangle (often used in trigonometry):

Savannah Anderson · Answer

undefined To find the length of the side of the square, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the diagonal in this case) is equal to the sum of the squares of the other two sides (the sides of the square).

Let's denote the length of the side of the square as "s". Using the Pythagorean theorem, we have:

s^2 + s^2 = (12√2)^2

2s^2 = 288

Dividing both sides by 2:

s^2 = 144

Taking the square root of both sides:

s = √144

Therefore, the length of the side of the square is 12 ft.