In triangles △ABC and △DEF, m∠A=m∠E, m∠C=m∠F, AC=6, EF=2, and AB=3.3, side

DF

is shorter than side

BC

by 3.2. Find the unknown sides of these triangles.

BC = 4.8

DE = 1.1

DF = 1.6

Step-by-step explanation:

In ΔABC and ΔDEF

∴ m∠A = m∠E

∵ m∠C = m∠F

∴ m∠B = m∠D

∴ ΔABC similar to ΔEDF

∴ AB/ED = BC/DF = AC/EF

∵ AC = 6 and EF = 2

∵ DF = BC - 3.2

∵ AB = 3.3

∴ 3.3/ED = BC / (BC - 3.2) = 6/2

∴ ED = (3.3 * 2) : 6 = 1.1

∴ 2BC = 6 (BC - 3.2) ⇒ 2BC = 6BC - 19.2 ⇒ 4BC = 19.2

∴ BC = 4.8

∴ DF = 4.8 - 3.2 = 1.6