A 25-foot ladder leans against a wall so that it is 20 feet high at the top. The ladder is moved so that the base of the ladder travels toward the wall twice the distance that the top of the ladder moves up. How much higher is the top of the ladder now? (Hint: Let 15−2x be the distance from the base of the ladder to the wall.)

Therefore the top of the ladder moves up 4 ft.

Explanation:

Given that a 25 foot ladder incline against a wall. So the top of it is 20 feet high.

It forms a right angled triangle.

Here Altitude = 20 foot,  hypotenuses= 25 feet

Let the base = x

We applying the Pythagorean Theorem

Altitude²+ base²= hypotenuses²

⇒20²+x²= 25²

⇒x²= 625-400

⇒x²= 225

⇒x=15 foot

The distance between the bottom of the ladder and wall is 15 feet.

Again given that, the ladder is moved so that ladder travels toward wall twice the distance that the top of the ladder moves up.

Consider the top of the ladder moves up y feet.

So, The bottom of the ladder moves towards wall = 2y.

(15-2y) feet is the distance between the wall and the bottom of the ladder.

And the top of the ladder is = (20+y)

Now base = 15-2y, altitude = 20+y and hypotenuse = 25

Applying Pythagorean Theorem,

(20+y)²+(15-2y)²=25²

⇒400+40y+y²+225-60y+4y²=625

⇒5y²-20y+625=625

⇒5y²-20y=0

⇒5y(y-4)=0

⇒y=0,4

y=0 does not make sense.

∴y=4 ft

Therefore the top of the ladder moves up 4 ft.

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