SOLUTION: A ladder of length 26ft is placed against a building in such a way that the distance from the top of the ladder to the ground is 14ft more than the distance from the bottom of the

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Question 805914: A ladder of length 26ft is placed against a building in such a way that the distance from the top of the ladder to the ground is 14ft more than the distance from the bottom of the ladder to the building. Find both distances.
i thought i would use a^2 + b^2=c^2 the pythagoreum theory
a^2 + 14ft^2 =26ft^2
but the problem says 14 ft more so i wasn't sure if that equation was correct.
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
A ladder of length 26ft is placed against a building in such a way that the distance from the top of the ladder to the ground is 14ft more than the distance from the bottom of the ladder to the building.
Find both distances.
i thought i would use a^2 + b^2=c^2 the pythagoreum theory
:
You are close to right, however:
a = dist from the ladder to the building
"14ft more" means that:
(a+14) = ground to the point the ladder rests on the building
therefore
a^2 + (a+14)^2 = 26^2
FOIL (a+14)(a+14)
a^2 + a^2 + 28a + 196 = 676
2a^2 + 28a + 196 - 676 = 0
2a^2 + 28a - 480 = 0
simplify divide by 2
a^2 + 14a - 240 = 0
Factors to
(a+24)(a-10) = 0
The positive solution is all we want here
a = 10 ft, the base of the ladder to the building
10+14 = 24 ft, top of the ladder to the ground
:
:
Check that on a calc; enter