Answer:
The top of the ladder is now at 10 ft.
Step-by-step explanation:
At the start, we have a height H=6, a length L=10 and a base B, that has to be calculated by the Pythagorean theorem:
[tex]B^2=L^2-H^2=10^2-6^2=100-36=64\\\\B=\sqrt{64}=8[/tex]
The base is moved twice the distance the height moves up.
We called this distance x, so we have:
[tex]L^2=(H+x)^2+(B-2x)^2=H^2+2Hx+x^2+B^2-4Bx+4x^2\\\\L^2=(H^2+B^2)+5x^2+(2H-4B)x\\\\L^2=L^2+5x^2+(2H-4B)x\\\\0=5x^2+(2H-4B)x\\\\5x+(2H-4B)=0\\\\x=\dfrac{4B-2H}{5}=\dfrac{4*8-2*6}{5}=\dfrac{32-12}{5}=\dfrac{20}{5}=4[/tex]
The new height (H+x) is
[tex]H'=H+x=6+4=10[/tex]
The base travels 2x=8, so the new base B' is 0.
This means that the ladder is all against the wall (L=H').
