Answer:
c) 5√2 cm
Step-by-step explanation:
A square with side length l has a perimeter given by the following equation:
P = 4l.
In this question:
P = 20
So the side length is:
4l = 20
l = 20/4
l = 5
Diagonal
The diagonal forms a right triangle with two sides, in which the diagonal is the hypothenuse. Applying the pytagoras theorem.
[tex]d^{2} = l^{2} + l^{2}[/tex]
[tex]d^{2} = 5^{2} + 5^{2}[/tex]
[tex]d^{2} = 50[/tex]
[tex]d = \pm \sqrt{50}[/tex]
Lenght is a positive meausre, so
[tex]d = \sqrt{50}[/tex]
[tex]d = \sqrt{2 \times 25}[/tex]
[tex]d = \sqrt{2} \times \sqrt{25}[/tex]
[tex]d = 5\sqrt{2}[/tex]
So the correct answer is:
c) 5√2 cm
