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TheStunter
a fost răspuns

In triunghiul dreptunghic MNP,m(∡M)=90°,MQ⊥NP,Q∈ (NP),se da:
a)PQ=6,4 cm si NP=10 cm.Calculati NQ,MN si MP.

Răspuns :

Crisanemanuel
a)NQ=NP-PQ=10-6,4=3,6cm→NQ=3,6cm
inΔMNP aplicam teorema inaltimii:MQ²=NQ×QP⇒MQ=√NQ×QP
MQ=√3,6×6,4=√23,04=4,8cm→MQ=4,8cm
inΔMNQ aplic Th.Pitagora⇒MN²=NQ²+MQ²⇒MN=√(3,6)²+(4,8)²=
=√12,96+23,04=√36=6cm→MN=6 cm
inΔQMP aplic Th. Pitagora:MP²=MQ²+QP²⇒MP=√(4,8)²+(6,4)²=
=√23,04+40,96=√64=8 cm→MP=8cm

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