SOLUTION: A ladder is leaning against a wall. The distance from the bottom of the ladder to the wall is 3 feet less than the length of the ladder. Find the length of the ladder, if the dista
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Question 145407: A ladder is leaning against a wall. The distance from the bottom of the ladder to the wall is 3 feet less than the length of the ladder. Find the length of the ladder, if the distance of its top to the ground is 4 feet less than the length of the ladder.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A ladder is leaning against a wall. The distance from the bottom of the ladder to the wall is 3 feet less than the length of the ladder. Find the length of the ladder, if the distance of its top to the ground is 4 feet less than the length of the ladder.
:
Using the formula a^2 + b^2 = c^2
:
Let x = length of the ladder (c)
:
"The distance from the bottom of the ladder to the wall is 3 feet less than the length of the ladder." Therefore:
(x-3) = a
:
"the distance of its top to the ground is 4 feet less than the length of the ladder." therefore:
(x-4) = b
:
Using the formula we have:
(x-3)^2 + (x-4)^2 = x^2
FOIL
(x^2 - 6x + 9) + (x^2 - 8x + 16) = x^2
:
Combine like terms on the left
x^2 + x^2 - x^2 - 6x - 8x + 9 + 16 = 0
:
x^2 - 14x + 25 = 0
:
Solve for x using the quadratic formula;
a=1; b=-14; c=25
:
:
you can do the math here, the reasonable solution is x = 11.9' length of ladder
:
:
Check solution
8.9^2 + 7.9^2 = 141.6 which is 11.9 squared
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