Question

∆ABC~∆DEF such that AB =9.1 cm and DE= 6.5cm .If the perimeter of∆DEFnis 25 cm , what is the perimeter of∆ ABC

Answer 1

Given:- Triangle ABC congruent Triangle DEF
AB=9.1, DE=6.5,Perimeter of Triangle DEF = 25cm
To prove:- Find perimeter of Triangle ABC
Proof:- Triangle ABC ~ DEF (Given)
:• Angle A = Angle F
Angle B = Angle E
Angle C = Angle D
Perimeter of Triangle DEF = 25 cm
EF+DE+FD=25cm
9.1+6.5+FD=25cm
15.6+FD=25cm
FD=25-15.6cm
FD=9.4cm
:• EF=AB=9.1cm
DE=BC=6.5cm
FD=AC=9.4cm
Hence,Perimeter of Triangle ABC
AB+BC+AC
9.1+6.5+9.4=25cm
Proved•

Answer 2

Answer:

Step-by-step explanation:

SOLUTION:-

➠ ΔABC ~ ΔDEF such that, AB=9.1cm and DE=6.5cm.

➠ ΔABC ~ ΔDEF (given)

➠ΔABC is congruent to ΔDEF ,since all sides & angle are congruent.

➠.°. AB = DE, BC=EF ,AC=DF & A =D ,B=E , C = F

➠in ΔDEF,

➠ DE + EF + DF =25

➠ 9.1+6.5 +DF =25

➠ .°.DF = 25-15.6

➠ .°. DF = 9.4cm.

[NOTE:- AC = DF , .°. AC = 9.4cm]

➠ in ΔABC,

➠ AB+BC+ AC

➠ 9.1+6.5+9.4

➠ 25cm