<PRE><B>Question 332729</B>
Initially, a 25-foot ladder 
24 feet from the ground. 
Nathan moves the base of the ladder by x feet
.
INITIAL POSITION
d^2= 25^2-24^2
d^2=625-576=49
d=7 feet.
..
AFTER SHIFTING
Let the ladder be shifted to 20 feet height .
let the foot of the ladder move x feet
The distance from the wall will be x+7 feet

..
ladder = 25 feet
lowered height vertically = 20 feet
..
(x+7)^2+20^2=25^2
x^2+14x+49+400=625
x^2+14x-176=0
x^2+22x-8x-176=0
x(x+22)-8(x+22)=0
(x+22)(x-8)=0
x= 8 feet.

Nathan moved the ladder on ground by 8 feet.
the ladder will be 8+7 =15 feet from the ground after shifting

..
CHECK
15^2+20^2=225+400=625 
sqrt 625 = 25 the length of the ladder</PRE>