SOLUTION: An extension ladder rests 4 m up a wall. If the ladder is extended a further 0.8 m without moving the foot of the ladder, then it will now rest 1 m further up the wall. How long is

Question 1127848: An extension ladder rests 4 m up a wall. If the ladder is extended a further 0.8 m without moving the foot of the ladder, then it will now rest 1 m further up the wall. How long is the extended ladder?
Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
So you have a right triangle where the long leg is the wall and the hypotenuse is the ladder (draw it, I did). The short leg of the triangle is the distance from the bottom of the wall to the bottom of the ladder.
:
So the problem says: when the hypotenuse increases by 0.8m the long leg increases by 1m. Let the hypotenuse be h and the short leg be x (we know the length of the long leg, it's the height of the wall and it goes from 4 to 5 m.)
x� + 4� = h�
x� = h� - 16 (1)
When the ladder is extended by h + 0.8 meters it reaches 5 meters up the wall:
x� + 5� = (h + 0.8)�
x� = (h + 0.8)� - 25 (2)
Combine equations (1) and (2):
(h + 0.8)� - 25 = h� - 16
(h + 0.8)� - h� = 25 - 16
h� + 0.64 - h� = 9
1.6h = 8.36
h = 8.36 � 1.6 = 5.225
The length of the extended ladder is: 5.225 + 0.8 = 6.025 meters.
:
Happy learning!
RELATED QUESTIONS
A ladder 5.6 m long rests against a vertical wall 8 m high. Calculate the distance of the (answered by ikleyn,greenestamps)

a 4 m ladder rests against a vertical wall with its foot 2m from the wall. How far up the (answered by josgarithmetic)

The foot of a ladder is placed 6 feet from a wall. If the top of the ladder rests 8 feet... (answered by solver91311,nerdybill)

(Pythogorean Theorem) The foot of a ladder is placed 6 feet from a wall. If the top of... (answered by stanbon)

The foot of a ladder is placed 6 feel from a wall. If the top of the ladder rests 8 feet... (answered by Boreal)

The foot of an extension ladder is 10 feet away from the base of a wall. The ladder is 2... (answered by checkley79,scott8148)

The foot of an extension ladder is 15 ft from a wall. The ladder is 5 ft longer than the (answered by Fombitz)

A ladder of length 8 m rests against a wall so that the angle between the ladder and the... (answered by Alan3354)

hi somebody please help me................................. i am in desperate need of... (answered by bucky,Earlsdon)