Question

Please help fast! WILL GIVE MEDAL
In parallelogram DEFG, DH=x+1, HF=3y, GH=3x-4, and HE=5y+1. Find the values of x and y. The diagram is now drawn to scale.

Answer 1

first, we gather our givens:
\[DH = HF \rightarrow x + 1 = 3y\]
\[GH = HE \rightarrow 3x - 4 = 5y + 1\]
then we isolate y:
\[y = \frac{ x + 1 }{ 3 }\]
\[y = \frac{ 3 }{ 5 } x - 1\]
next we equate both expressions like so:
\[\frac{ x }{ 3 } + \frac{ 1 }{ 3 } = \frac{ 3 }{ 5 } x - 1\]
now we solve for x:
\[4 = \frac{ 4 }{ 5 } x\]
\[5 = x\]
plug x back into either equation:
\[y = \frac{ 3 }{ 5 } (5) - 1 = 3 - 1 = 2\]

so there you have it
\[x = 5\]
\[y = 2\]

Answer 2

Thanks so much!!!(: