SOLUTION: I need help with a word problem: The foot of an extension ladder is approximately 10 ft for a wall. The height that the ladder reaches on the wall and the length of the ladder

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Question 440786: I need help with a word problem:
The foot of an extension ladder is approximately 10 ft for a wall. The height that the ladder reaches on the wall and the length of the ladder are consecutive intergers. How long is the ladder to the nearest foot?
Thanks in advance for your help
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
The foot of an extension ladder is approximately 10 ft for a wall. The height that the ladder reaches on the wall and the length of the ladder are consecutive intergers. How long is the ladder to the nearest foot?
.
Let x = height the ladder reaches on the wall
then
x+1 = height of ladder
.
x^2 + 10^2 = (x+1)^2
x^2 + 10^2 = (x+1)(x+1)
x^2 + 10^2 = x^2+2x+1
10^2 = 2x+1
100 = 2x+1
99 = 2x
49.5 ft = x
.
ladder then is:
x+1 = 49.5+1 = 50.5 feet