Question

Hey mate ❤️❤️

plz help me....



In the adjoining figure , ABC ~ DEFand their sides are of lengths (in cm)as marked along them. Find the length of the side. of a triangle.

Answer 1

ABC ~DEF

SO

AB/DE = BC/EF = AC/DF

AB= 2X -1

DE = 18

BC = 2X +2

EF = 3X +9

AC= 3X

DF = 6X

SO

AB/DE = AC/DF

2X -1)/ 18 = 3X/6X


2X - 1)/ 18 = 3/6 = 1/2

2( 2X -1) = 18

4X -2 = 18

4X = 20

X= 5


SO AB= 2X -1 = 9

DE = 18

BC = 2X +2 = 12

EF = 3X +9 = 24

AC= 3X = 15

DF = 6X = 30

Answer 2

if ∆ABC ~∆DEF

then , AB/DE = BC/EF = AC/DF

=> 2x-1 / 6x = 2x+2/3x+9 = 3x/18

first ,

=> 2x-1 / 6x = 2x+2/3x+9

=>( 2x-1 )×(3x+9) = (2x+2) ×6x

=> 6x²+18x-3x -9 = 12x² + 12x

=> 12x²-6x² +12x+3x -18x +9 =0

=> 6x² -3x +9 =0

=> 2x²-x + 3 = 0

d = (-1)² -4×2×3 = -23<0
so , haven't any real value. ,


now ,

=> 2x-1 / 6x = 3x/18

=> (2x-1) ×18 = 6x × 3x

=> 36x -18 = 18x²

=> 18x² -36x +18 =0

=> x² -2x +1 =0

=> x²-x-x +1=0

=> x(x - 1) - 1(x - 1) =0

=> so , x = 1

put 1 at instead of x and find length .

hope its help you