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

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

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Answer 1 · 2016-03-07T04:44:15

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

Explanation:

$P = 4 c$ $P = 4c$

$12 = 4 c$ $12 = 4c$

$3 = c$ $3 = c$

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.

$a^{2} + b^{2} = c^{2}$ $a^2 + b^2 = c^2$

$3^{2} + 3^{2} = c^{2}$ $3^2 + 3^2 = c^2$

$9 + 9 = c^{2}$ $9 + 9 = c^2$

$18 = c^{2}$ $18 = c^2$

$\sqrt{18} = c$ $sqrt(18) = c$

$3 \sqrt{2} = c$ $3sqrt(2) = c$

The diagonal measures $3 \sqrt{2}$ $3sqrt(2)$ cm.

Practice exercises:

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 $x - 2$ $x - 2$ , $x - 2$ $x - 2$ and $2 x + 1$ $2x + 1$ . Its perimeter is 41. Find the height of the triangle.

Good luck!

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

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