Trikotnik ABC je podoben trikotniku PQR. AB ustreza PQ in BC ustreza QR. lf AB = 9, BC = 12, CA = 6 in PQ = 3, kakšne so dolžine QR in RP?

Trikotnik ABC je podoben trikotniku PQR. AB ustreza PQ in BC ustreza QR. lf AB = 9, BC = 12, CA = 6 in PQ = 3, kakšne so dolžine QR in RP?
Anonim

Odgovor:

# QR = 4 # in # RP = 2 #

Pojasnilo:

Kot # DeltaABC ~~ DeltaPQR # in # AB # odgovarja # PQ # in # BC # odgovarja # QR #, imamo,

Potem imamo

# (AB) / (PQ) = (BC) / (QR) = (CA) / (RP) #

Zato # 9/3 = 12 / (QR) = 6 / (RP) #

t.j. # 9/3 = 12 / (QR) #

ali # QR = (3xx12) / 9 = 36/9 = 4 #

in # 9/3 = 6 / (RP) #

ali # RP = (3xx6) / 9 = 18/9 = 2 #