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

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.

$d^{2} = l^{2} + l^{2}$

$d^{2} = 5^{2} + 5^{2}$

$d^{2} = 50$

$d = \pm \sqrt{50}$

Lenght is a positive meausre, so

$d = \sqrt{50}$

$d = \sqrt{2 \times 25}$

$d = \sqrt{2} \times \sqrt{25}$

$d = 5\sqrt{2}$

So the correct answer is:

c) 5√2 cm