a ladder leans against a awall.The top of the ladder is 8 feet above the ground. If the botttom of the ladder is then moved 2 feet farther from the wall, the ladder will lie on the ground with its toptouching the wall. How long is the ladder?

Question

a ladder leans against a awall.The top of the ladder is 8 feet above the ground. If the botttom of the ladder is then moved 2 feet farther from the wall, the ladder will lie on the ground with its toptouching the wall. How long is the ladder?

Answer 1

Assistance needed.

Please type your subject in the School Subject box. Any other words are likely to delay responses from a teacher who knows that subject well.

Answer 2

let b be the base, h the height, and l the length.

b^2+8^2=L^2
and b+2=L so b=L-2
THEN
(L-2)^2+8^2=L^2
solve for L

Answer 3

ok my B

i was just sorta needy of an answer quickly bcuz i gotta turn this in tomorrow
thanks

Answer 4

Thanks man!!!

Answer 5

To find the length of the ladder, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Let's label the length of the ladder as "L", the distance from the bottom of the ladder to the wall as "x", and the height of the ladder from the ground to the top as "8".

In the first scenario, the ladder is leaning against the wall. We know that the top of the ladder is 8 feet above the ground. This forms a right triangle, with the ladder as the hypotenuse, the distance from the bottom to the wall as one leg, and the height of the ladder as the other leg.

Using the Pythagorean theorem, we can write the equation:

L^2 = x^2 + 8^2

Now, in the second scenario, the bottom of the ladder is moved 2 feet farther from the wall. This means the distance from the bottom to the wall is now (x + 2) feet. Also, the ladder lies on the ground with its top touching the wall, which means the height is now 0 feet.

Using the Pythagorean theorem again, we can write the equation:

L^2 = (x + 2)^2 + 0^2

Since the length of the ladder is the same in both scenarios, we can set the two equations equal to each other:

x^2 + 8^2 = (x + 2)^2 + 0^2

Expanding and simplifying the equation, we get:

x^2 + 64 = x^2 + 4x + 4

Now, let's solve for x:

x^2 - x^2 + 4x = 4 - 64
4x = -60
x = -15

However, we are dealing with a physical measurement, so we can discard the negative value. Therefore, x = 15.

Now, substituting this value of x back into either equation, we can find the length of the ladder:

L^2 = 15^2 + 8^2
L^2 = 225 + 64
L^2 = 289
L = √289
L = 17

So, the length of the ladder is 17 feet.