25^2-7^2=576
it means that the height is equal to 24.

since the top of the ladder slips down 4 feet, then the height of the wall =24-4=20

the bottom =sqrt(25^2-20^)=sqrt(625-400)=15

ans is E , not C
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New,total distance between foot ladder and the wall = 15
slip = 15-7 = 8 hence C

We have a right triangle with the hypotenuse of 25 feet and the base of 7 feet, hence its the height is \(\sqrt{25^2-7^2}=24\) feet;

Since the top of the ladder slips down 4 feet then the new height becomes 24-4=20 feet and the new base becomes \(\sqrt{25^2-20^2}=15\) feet;

Question basically asks about the difference between the old base and the new base, which is 15-7=8 feet.

Answer: C.
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Initially, base (Point E) of 25 feet long ladder (AE) is 7 meter away from the base of wall (Point B).

height of the top point (A) can be found using Pythagoras Theorem

AB = sqrt(AE^2-BE^2)
= sqrt (25^2-7^2) = sqrt (625-49) = sqrt(576) =24

When the top of the ladder slips 4 meter, height of top point reduces by 4 meter.
Now, as per diagram, DC is ladder and BD is height of top point and BC is the distance of base of ladder from wall.

we have , DC = 25, BD = 24-4 = 20,

By Pythagoras theorem, BC = sqrt (DC^2-BD^2) = sqrt (25^2-20^2) = sqrt(625-400)=sqrt (225) = 15

base point has slipped by a distance EC which can be found by subtracting BE from BC

EC = BC-BE = 15-7 = 8 .
Hence option C is the answer.

you can think of this like a triangle problem where the height and base change but the hypotenuse remains the same (25)

so at first the ladder's base is 7, with a hypotenuse of 25 you can use the Pythagorean theorem to figure out that the height is 24.

The new height is then 20, with a hypotenuse of 25, which is a version of the 3:4:5 common right triangle, so we know the new base is 15.

Its important to keep in mind what you are looking for (how far the ladder slips) otherwise you might incorrectly pick 15 at this point. However, the correct answer is 15-7 or 8 (C)
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Ladder Before Movement
-------------
25^2 = 7^2 + x^2
625=49+x^2
x^2=24

Ladder After Movement
--------------------
25^2=20^2+x^2
625=400+x^2
225=x^2
x=15

Ladder moved 15-7 = 8 feet

C

The ladder will from a right angled triangle with the wall. The hypotenuse will be 25 feet and base will be 7 feet.
So the perpendicular =\sqrt{25^2-7^2} = \sqrt{576} = 24 feet

When the top of the ladder slips by 4 feet the perpendicular will be = (24- 4) feet = 20 feet
But the length of the ladder that is the hypotenuse will remain the same.

In this case the base will be =\sqrt{25^2 - 20 ^2} = 15 feet

So the distance from the base of the ladder to base of the wall will become = 15 ft
So the ladder slips by (15-7) ft = 8 ft (C)

The most difficult aspect of this is getting your head around what actually happens.
The ladder's length doesn't change, but it's distance in relation to the wall does when the ladder "slips down".

Imagine a ladder propped up against a wall and the base gets kicked out such that the ladder is still up against the wall, but the base is now further out.

This is the scenario.
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Original ladder placement = \(25^2 = 7^2 + b^2\)

\(b^2 = 576; b = 24\)

Since the ladder slips down by \(4 feet, b - 4 = 20\)

\(a^2 + 20^2 = 25^2\)

\(a^2 = 225\)

\(a = 15\)

The bottom of the ladder is 15 feet from the wall.

\(15 - 7 = 8\)

The ladder slipped 8 feet. The answer is C.
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With the Ladder up against the Perpendicular Wall, we have a Right Triangle:

Ladder Length = 25 = Hypotenuse

Ground = Bottom Leg = 7 feet

From the 90 degree Vertex to the Vertex where the Ladder meets the Wall = Leg 2 = X

x - 7 - 25 ------> this is the Pythagorean Triplet of: 7 - 24 -25


The Height from the Ground up to the Point where the ladder meets the wall is thus = 24 feet

When the ladder slips down -4 Feet, we know have a new Right Triangle:

Leg = 20 feet

Hypotenuse = ladder length = 25 feet

and new Distance on the Grounds = X = Leg

Using Pythagoras:

(X)^2 + (20)^2 = (25)^2

(X)^2 = (25)^2 - (20)^2

(X)^2 = (25 + 20) (25 - 20)

(X)^2 = (45)(5) -----> (9)*(25)

Sqrt( X'2) = Sqrt( 9 * 25 )

X = 15

The Ladder Slipped Down: 15 Feet - 7 feet = 8 feet further

-C-

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I understand the theory behind this question. However, does anyone have any tips on how to answer it in under 2 minutes?

For example, finding the square root of 576? Under exam conditions my mind will panic and freeze seeing that in front of me.