In parallelogram defg,, DH = x+3 HF= 3y GH=3x-3 and HE =5y + 4

Answer:The value of x and y is 9 and 4 unitsSolution: We have,  DH = x+3; HF= 3y and GH=3x-3; HE =5y + 4 For parallelogram, we know that, DH=HF So, [tex](x+3)=3 y\Rightarrow x=(3 y-3)[/tex]--------- (i) Again, GH = HE So, [tex]3x-3 = 5y +4[/tex][tex]\Rightarrow3 x=5 y+4+3[/tex][tex]x = \frac{(5y+7)}{3}[/tex] ………. (ii) Now equating both (i) and (ii) we get, [tex]\Rightarrow3 y-3=\frac{5 y+7}{3}[/tex][tex]\Rightarrow3\times(3y-3) = 5y+7[/tex][tex]\Rightarrow9y - 9 = 5y +7[/tex][tex]\Rightarrow9y-5y=7+9[/tex][tex]\Rightarrow4y = 16[/tex][tex]\Rightarrow y = 4[/tex]So the value of [tex]x = 3\times4 -3 = 9[/tex]The value of x and y is 9 and 4  units