A diagonal of a square is 10 cm long. How do you find the length of each side of the square?

1 Answer
Oct 13, 2015

Answer:

The side of the square is #5sqrt(2)#

Explanation:

Start from a square #ABCD#. Now consider the triangle #ABC#. It's a right triangle, whose catheti are the sides of the square, and whose hypotenuse is the diagonal of the square.

Now, Pythagoras' theorem tells us that

#overline(AB)^2 + overline(BC)^2 = overline(AC)^2#

But #AB# and #BC# are both sides of the square, and then they both equal a certain quantity #l#, while #AC# is the diagonal and equals #10# cm. The previous identity becomes

#2d^2 = 100 \implies d^2 = 50 \implies d=sqrt(50)#

If you like it, you can simplify #sqrt(50)# into #sqrt(25*2)=sqrt(25)*sqrt(2)=5sqrt(2)#.