Question

1. O perímetro de um quadrado é 20 cm. Determine sua diagonal. 1 ponto a) 2 √5 cm b) 20√2 cm c) 5√2 cm d) 2√10 cm

Answer 1

c) 5√2 cm

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.

`d^(2) = l^(2) + l^(2)`

`d^(2) = 5^(2) + 5^(2)`

`d^(2) = 50`

`d = \pm √(50)`

Lenght is a positive meausre, so

`d = √(50)`

`d = √(2 * 25)`

`d = √(2) * √(25)`

`d = 5√(2)`

So the correct answer is:

c) 5√2 cm