Question

W is the midpoint of DY. If `DW=x^2 +4x` and `WY=4x+16`, how do you find DY?

Answer 1

Provided the lengths are non-zero
`color(white)("XXX")color(green)(abs(DY)=64)`

Explanation:

If `W` is the midpoint of `DY` then
`color(white)("XXX")abs(DW)=abs(WY)`

`color(white)("XXX")x^2+4x=4x+16`

`color(white)("XXX")x^2=16`

`color(white)("XXX")x=+-4`

If `x=-4`
`color(white)("XXX")x^2+4x=0 and 4x+16=0`
so the total length `abs(DY)=abs(DW)+abs(WY)=0`

If `x=+4`
`color(white)("XXX")x^2+4x=32 and 4x+16=32`
so the total length `abs(DY)=abs(DW)+abs(WY)=32+32=64`