Pentagon

The signboard has the shape of a pentagon ABCDE, in which the line BC is perpendicular to the line AB and EA is perpendicular to the line AB. Point P is the heel of the vertical starting from point D on line line AB. | AP | = | PB |, | BC | = | EA | = 6dm, | PD | = 8.4dm. The point X - the intersection of the lines PE and DA, the point Y - the intersection of the lines PC and BD is marked on the shield. I need to focus the point Z, which is the intersection of the lines XY and PD. Specify | PZ |.

Correct answer:

z =  3.5 dm

Step-by-step explanation:

a=6 dm b=8.4 dm  a:(A+B)=z:B b:(A+B)=z:A  a B=z A+z B b A=z A+z B  a B=b A A:B=a:b  a:(A+B)=z:B  z=a A+BB z=a A/B+11  z=a a/b+11=6 6/8.4+11=27=3.5=27 dm=3.5 dm   Verifying Solution:   z2=b 1+b/a1=8.4 1+8.4/61=27=3.5 dm



Did you find an error or inaccuracy? Feel free to write us. Thank you!



avatar







Tips to related online calculators
Looking for calculator of harmonic mean?
Looking for a statistical calculator?
Check out our ratio calculator.
See also our right triangle calculator.
See also our trigonometric triangle calculator.

 
We encourage you to watch this tutorial video on this math problem: video1

Related math problems and questions: