Pentagon

The signboard has the shape of a pentagon ABCDE, in which line BC is perpendicular to line AB, and EA is perpendicular to line AB. Point P is the heel of the vertical starting from point D on line AB. | AP | = | PB |, | BC | = | EA | = 6dm, | PD | = 8.4dm. 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



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