Question

Triunghiul abc este dreptunghic in A si M este mijlocul cateti [AC].stiind ca AB=4CM si BM= 5 cm,determinati lungimea ipotenuzei

Answer 1

AB=4CM=> AB=4AM => AM=AB/4. fie tr dreptunghic BAM , aplicam th pitagora=> AB²=BM²-AM²=> AB²=25-AB²/16=> 16 AB²=400-AB² => 17AB²=400 => AB²=400/17 => AB=√400/√17 =>AB=20√17/17. =< AM=AB/4=> AM=5√17/17=>AC=2*5√17/17=10√17/17. Fie tr ABC => conf th pitagora BC²=AB²+AC²=400/17+100/17=500/17=> BC=10√5/√17=> BC=10√85/17