Question

PLEASE HELP ME ASAP!!!!

Part A: Identify the diagonals in the parallelogram.

Part B: Determine the value for x and y. Show your work.

Part C: Identify the length of each diagonal. Show your work.

Answer 1

Part A

`\overline{AC}` and
`\overline{BD}`

Part B

Diagonals of a parallelogram bisect each other, so

`BE=ED \implies 2x+3=3y-4 \implies 3y=2x+7 \implies y=(2)/(3)x+(7)/(3)\\\\AE=EC \implies y+4=4x-6 \implies y=4x-10`

Solving by substitution,

`(2)/(3)x+(7)/(3)=4x-10`

Multiplying both sides by 3,

`2x+7=12x-30\\\\37=10x\\\\x=3.7`

So,
`y=(2)/(3)\left((37)/(10) \right)+(7)/(3)=(24)/(5)`

Part C

`BE=ED=2(3.7)+3=10.4\\\\AE=EC=4(3.7)-6=8.8`

`\therefore BD=2(10.4)=20.8, AC=2(8.8)=17.6`