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

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
RELATED QUESTIONS
A 20 foot ladder is placed against a building in such a way that the distance from the... (answered by mananth)

A ladder of length 15 ft is placed against a building in such a way that the distance... (answered by terrtwo)

A ladder 25 feet long is placed against the side of a building in such a way that it... (answered by Alan3354,josgarithmetic,MathTherapy,ikleyn)

A 26ft ladder is placed against a vertical wall of a building , with the bottom of the... (answered by mananth)

A ladder is leaning against a building. The distance from the bottom of the ladder to the (answered by Paul)

A ladder is leaning against a building. The distance from the bottom of the ladder to the (answered by RAY100)

A ladder is leaning against a building. The distance from the bottom of the ladder to the (answered by Fombitz)

A ladder is leaning against a building. The distance from the bottom of the ladder to the (answered by robertb)

A ladder is leaning against a building. The distance from the bottom of the ladder to the (answered by fractalier)