Answer:
Part 1) [tex]{x^{2} -12x=0[/tex]
Part 2) The height of the pole is [tex]12\ ft[/tex]
Step-by-step explanation:
Let
x------> the length of the pole
y------> the length of the shadow
we know that
[tex]x=y+3[/tex]
[tex]y=x-3[/tex] -----> equation A
Applying the Pythagoras Theorem to find the distance (hypotenuse in a right triangle)
[tex]\sqrt{x^{2} +y^{2}}=x+3[/tex] -----> equation B
substitute equation A in equation B and solve for x
[tex]\sqrt{x^{2} +(x-3)^{2}}=x+3[/tex]
squared both sides
[tex]{x^{2} +(x-3)^{2}}=(x+3)^{2}[/tex]
[tex]x^{2} +x^{2}-6x+9=x^{2}+6x+9[/tex]
[tex]x^{2} -12x=0[/tex] -----> equation that represent the situation
solve for x
[tex]x^{2} =12x[/tex]
[tex]x=12\ ft[/tex]
