Question

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

Answer 1

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!