Question

Problema din imagine va rog!
(si desen)​

Answer 1

Răspuns:

Explicație pas cu pas:

ABCD patrat, AB=36cm.  AM/MD=5/7, ⇒AM/5=MD/7=k, coeficient de prop.

⇒AM=5k, MD=7k, dar AM+MD=36, ⇒5k+7k=36, ⇒12k=36, ⇒k=3, deci

AM=5·3=15cm si MD=7·3=21cm.

La fel, AN/NB=4/5, ⇒AN/4=NB/5=c, coef. de prop. deci AN=4c, NB=5c, dar AN+NB=36, ⇒4c+5c=36, ⇒9c=36, ⇒c=4, deci AN=4·4=16cm, NB=5·4=20

Aria(ΔCMN)=Aria(ABCD)-(Aria(ΔAMN)+Aria(ΔMDC)+Aria(ΔBCN))

Aria(ABCD)=AB²=36²=1296cm²;  Aria(ΔAMN)=(1/2)·AM·AN=(1/2)·15·16=120;

Aria(ΔMDC)=(1/2)·MD·DC=(1/2)·21·36=21·18=378; Aria(ΔBCN)=(1/2)·BC·BN= (1/2)·36·20=360. Deci

Aria(ΔCMN)=1296-(120+378+360)=1296-858=438cm²