A square has a perimeter of 12 centimeters. How do you find the length of the diagonal of the square?

1 Answer
Noah G
Mar 7, 2016

The perimeter of a square is found by the formula #P = 4c#

Explanation:

#P = 4c#

#12 = 4c#

#3 = c#

Since all the sides in a square are equal in length, the diagonals are equal in length. By Pythagoras Theorem we can find the length of one of the diagonals.

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

#3^2 + 3^2 = c^2#

#9 + 9 = c^2#

#18 = c^2#

#sqrt(18) = c#

#3sqrt(2) = c#

The diagonal measures #3sqrt(2)# cm.

Practice exercises:

  1. A square has an area of 64 square meters. Find the perimeter of the triangle that is formed between two the sides and one of the diagonals.

2 . A rectangle has a perimeter of 24 cm. The length measures 7 cm. Find the distance between the two corners of the rectangle (the length of a diagonal)

Challenge Problem:

An isosceles triangle has lengths of #x - 2#, #x - 2# and #2x + 1#. Its perimeter is 41. Find the height of the triangle.

Good luck!

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