Question

Does anyone know how to do this? Im so confused.

Answer 1

Answer:  PC = 5

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Work Shown:

AB+BC+CD = AD .... segment addition postulate

BC+BC+CD = AD ... replace AB with BC (since AB = BC)

BC+BC+BC = AD ... replace CD with BC (since BC = BC)

3*BC = AD .... combine like terms

3*BC = 12 .... replace AD with 12

BC = 12/3 .... divide both sides by 3

BC = 4

For right triangle PBC, the legs are BP = 3 and BC = 4. We can use the Pythagorean Theorem to find that the hypotenuse is PC = 5

The steps are shown below

(BP)^2+(BC)^2 = (PC)^2

3^2+4^2 = (PC)^2

9+16 = (PC)^2

25 = (PC)^2

(PC)^2 = 25

PC = sqrt(25)

PC = 5

The other parts of the diagram seem to be thrown in as a distraction.