Question

Fie punctele M(-2;2), N (1;2) , P(1;6), Q(-2;6). Aflați perimetrul patrulaterului MNPQ .

Urgent!!​

Answer 1

$mn = \sqrt{(1 + 2) {}^{2} + {(2 - 2)}^{2} } = \sqrt{3 {}^{2} + {0}^{2} } = \sqrt{ {3}^{2} } = 3$

Deci MN=3CM

$np = \sqrt{(1 - 1) {}^{2} + (6 - 2) {}^{2} } = \sqrt{0 + {4}^{2} } = \sqrt{ {4}^{2} } = 4$

Deci NP=4 CM

$pq = \sqrt{( - 2 - 1) {}^{2} + (6 - 6) ^{2} } = \sqrt{( - 3)^{2} } = 3$

Deci PQ=3CM

$mq = \sqrt{( - 2 - 2) {}^{2} +(6 - 2) {}^{2} } = \sqrt{( - 4) {}^{2} + 4 {}^{2} } = \sqrt{4 {}^{2} + 4 {}^{2} } = \sqrt{2 \times {4}^{2} } = 4 \sqrt{2}$

Deci MQ=4 RADICAL DIN 2 CM

P(MNPQ)=MN+NP+QP+MQ=3+4+3+4 RADICAL DIN 2=2•3+2•2(1+RADICAL DIN 2)=2[3+2(1+ RADICAL DIN 2)]