Question

A) Analisando os pontos A(3, 3) B(-4, 2) C(-2, -2) D(4, -4), então determine o perímetro do quadrilátero ABCD.

Answer 1

Explicação passo-a-passo:

Temos que:

$\bullet~~\overline{AB}=\sqrt{(3+4)^2+(3-2)^2}$

$\overline{AB}=\sqrt{7^2+1^2}$

$\overline{AB}=\sqrt{49+1}$

$\overline{AB}=\sqrt{50}$

$\overline{AB}=5\sqrt{2}$

$\bullet~~\overline{BC}=\sqrt{(-4+2)^2+(2+2)^2}$

$\overline{BC}=\sqrt{(-2)^2+4^2}$

$\overline{BC}=\sqrt{4+16}$

$\overline{BC}=\sqrt{20}$

$\overline{BC}=2\sqrt{5}$

$\bullet~~\overline{CD}=\sqrt{(-2-4)^2+(-2+4)^2}$

$\overline{CD}=\sqrt{(-6)^2+2^2}$

$\overline{CD}=\sqrt{36+4}$

$\overline{CD}=\sqrt{40}$

$\overline{CD}=2\sqrt{10}$

$\bullet~~\overline{AD}=\sqrt{(3-4)^2+(3+4)^2}$

$\overline{AD}=\sqrt{(-1)^2+7^2}$

$\overline{AD}=\sqrt{1+49}$

$\overline{AD}=\sqrt{50}$

$\overline{AD}=5\sqrt{2}$

Perímetro é a soma dos lados

O perímetro desse quadrilátero é:

$P=\overline{AB}+\overline{BC}+\overline{CD}+\overline{AD}$

$P=5\sqrt{2}+2\sqrt{5}+2\sqrt{10}+5\sqrt{2}$

$P=10\sqrt{2}+2\sqrt{5}+2\sqrt{10}$

$P=2\cdot(5\sqrt{2}+\sqrt{5}+\sqrt{10})$