SOLUTION: A ladder is leaning against a house with its bottom 15 feet from the house. When the bottom of the ladder is pulled 9 feet further away from the house, the upper end slides 13 feet

Question 238728: A ladder is leaning against a house with its bottom 15 feet from the house. When the bottom of the ladder is pulled 9 feet further away from the house, the upper end slides 13 feet down. How many feet long is 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 house with its bottom 15 feet from the house.
When the bottom of the ladder is pulled 9 feet further away from the house, the upper end slides 13 feet down.
How many feet long is the ladder?
:
This is just a pythag problem: a^2 + b^2 = c^2
Where
a = height the ladder is on the building
b = 15'
c = length of the ladder
The equation:
a^2 + 15^2 = c^2
a^2 + 225 = c^2
:
:
The ladder slips down 13' and out 9' from the building,
(a-13) = height of the ladder on the building
b = 15 + 9 = 24'
c = length of the ladder, (unchanged)
:
the new equation:
(a-13)^2 + 24^2 = c^2
FOIL, square 24;
(a^2 - 26a + 169) + 576 = c^2
a^2 - 26a + 745 = c^2
:
Both equation = c^2, therefore:
a^2 + 225 = a^2 - 26a + 745
0 = a^2 - a^2 - 26a + 745 - 225
0 = -26a + 520
+26a = 520
a =
a = 20 ft, the original height of the ladder on the building
:
Find the length of the ladder (c)
c^2 = 20^2 + 15^2
c^2 = 400 + 225
c^2 = 625
c =
c = 25 ft is the ladder length
;
;
Check the solution when ladder slips down, ladder length should be the same
c^2 = (20-13)^2 + (25+9)^2
c^2 = 7^2 + 24^2 =
c^2 = 49 + 576
c^2 = 625
c = 25'; confirms our solution

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