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
