SOLUTION: When rescuing a woman from a burning building, fireman found that the height of the window she was leaning out of was 1m less than the length of the ladder. The distance from the f

Question 450110: When rescuing a woman from a burning building, fireman found that the height of the window she was leaning out of was 1m less than the length of the ladder. The distance from the foot of the ladder to the building was 8m less than the length of the ladder. Find the length of the ladder.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
When rescuing a woman from a burning building, fireman found that the height of
the window she was leaning out of was 1m less than the length of the ladder.
The distance from the foot of the ladder to the building was 8m less than the length of the ladder.
Find the length of the ladder.
:
Let x = length of the ladder
then
(x-1) = height of the window
and
(x-8) = distance from building to base of the ladder
:
This forms a right triangle we can solve, a^2 + b^2 = c^2
In this problem
x = c, the hypotenuse
(x-1) = a
(x-8) = b
;
so we have
(x-1)^2 + (x-8)^2 = x^2
;
FOIL
(x^2 - 2x + 1) + (x^2 - 16x + 64) = x^2
:
Combine like terms
x^2 + x^2 - x^2 - 2x - 16x + 1 + 64 = 0
:
a quadratic equation
x^2 - 18x + 65 = 0
:
Factors to
(x-5)(x-13) = 0
:
Two solutions but only one is reasonable
x = 13 meters is the length of the ladder
:
:
See if the works out
12^2 + 5^2 = 13^2
144 + 25 = 169, confirms our solution of x=13
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