Parallelogram. Find the length

[Avenger_0512]

1. GOAL is a parallelogram. GO= 3x+4, OA=2x-3, AL= 4x-10. Find the lengths of GO and GL.

 

[Otis]

GOAL is a parallelogram. GO= 3x+4, OA=2x-3, AL= 4x-10.

Hello Avenger. Something seems wrong with the exercise statement.

Opposite sides of a parallelogram are parallel (i.e., they have the same slope).

[imath]\overline{GO}[/imath] and [imath]\overline{AL}[/imath] are opposite sides, but the given slopes for those two line segments are different.



[imath]\;[/imath]

 

[The Highlander]

1. GOAL is a parallelogram. GO= 3x+4, OA=2x-3, AL= 4x-10. Find the lengths of GO and GL.

Further to what Otis points out, it really needs to be GA (not OA) that is 2x - 3 or the parallelogram will not construct! (See attached diagram.)

I would think the question ought to be (assigning AL the same gradient as GO):-

1. GOAL is a parallelogram. GO= 3x+4, GA=2x-3, AL= 3x-10. Find the lengths of GO and GL.
​

There's not much point attempting to answer the question unless you work with the suggested modifications.
Have you been given any answers? If an answer is provided (in the question paper) in may shed further light on the problem(s).

 

[pka]

1. GOAL is a parallelogram. GO= 3x+4, OA=2x-3, AL= 4x-10. Find the lengths of GO and GL.

Opposite sides of a parallelogram have the same length.
Therefore [imath]\|\overline{GO}\|=\|\overline{AL}\|~\&~\|\overline{GL}\|=\|\overline{AO}\|[/imath]
Thus [imath]2x+4=4x=10[/imath] so [imath]x=?~\&~\|\overline{GL}\|=?[/imath]
I have no clue what the other replies mean. But in basic middle school geometry [imath]\overline{GL}[/imath] is a line-segment.

 

[The Highlander]

Opposite sides of a parallelogram have the same length.
Therefore [imath]\|\overline{GO}\|=\|\overline{AL}\|~\&~\|\overline{GL}\|=\|\overline{AO}\|[/imath]
Thus [imath]2x+4=4x=10[/imath] so [imath]x=?~\&~\|\overline{GL}\|=?[/imath]
I have no clue what the other replies mean. But in basic middle school geometry [imath]\overline{GL}[/imath] is a line-segment.

Both Otis and I (naturally, IMNSHO) assumed that (in the absence of further, clear information) the expressions given were the equations of the lines the segments were part of. (See my diagram.)

If the problem had stated, for example, GO=3x+4 cm (or other unit of length) or just "units long" then it would have been clear that the question demanded solving for x.

I, for one, have never come across a line segment's length being expressed in this way but I bow to your greater experience in that area.

 

[pka]

Both Otis and I (naturally, IMNSHO) assumed that (in the absence of further, clear information) the expressions given were the equations of the lines the segments were part of. (See my diagram.)
If the problem had stated, for example, GO=3x+4 cm (or other unit of length) or just "units long" then it would have been clear that the question demanded solving for x.
I, for one, have never come across a line segment's length being expressed in this way but I bow to your greater experience in that area.

Did you read the whole list of questions?
In nos. 3 & 4, [imath]5x+23[/imath] is the measure of an angle as is [imath]6x-19[/imath].
I just guessed that the author was not a high functioning mathematician and simply meant a unknown.

 

[Otis]

[imath]2x+4=4x=10[/imath]

Oh, I see. You're interpreting the linear expressions as lengths.

In that case, I think you meant to type 3x+4 = 4x-10, above.



[imath]\;[/imath]