Drawing a parallelogram with side 4cm, diagonals summing to 11cm, angle 22°

[Redinorun]

I'd really need help with this. Thanks.

1. Homework Statement
Draw a parallelogram:
a = 4cm
e + f (diagonals) = 11cm
angle between a and e = 22°

Homework Equations

2 and 2 sides are parallel
both diagonals halve each other
(diagonal e goes from A to C)

The Attempt at a Solution

(attachment)

 

[ehild]

Go ahead with your attempt! You have drawn the blue triangle. PRS is isosceles. Halve the side RS and draw a perpendicular at the halfpoint. It defines point P.

ehild

 

[Redinorun]

Go ahead with your attempt! You have drawn the blue triangle. PRS is isosceles. Halve the side RS and draw a perpendicular at the halfpoint. It defines point P.

ehild
View attachment 74044

Thanks, got it. You're a life saver. By the way: Why wouldn't this work if a = 8cm? Is it because a would be longer than the sum of e and b (if we take half of it as a triangle)? Or is there another explanation?

 

[ehild]

a can not be longer than (e+f)/2. The yellow triangle would not exist.

 

[Redinorun]

a can not be longer than (e+f)/2. The yellow triangle would not exist.

View attachment 74049

Thank you! (I menth something like that, yes)