Question

A 25-foot ladder leans against a wall. The base of the ladder is 15 feet from the bottom of the wall. How far up the wall does the top of the ladder reach?

Answer 1

ANSWER

20ft

EXPLANATION

The ladder, the wall and the ground formed a right triangle.

Let how far up the wall does the top of the ladder reached be x units.

The 25ft ladder is the hypotenuse.

The shorter legs are, 15ft and x ft

Then from Pythagoras Theorem,

${x}^{2} + {15}^{2} = {25}^{2}$

${x}^{2} + 225 = 625$

${x}^{2}= 625 - 225$

${x}^{2}= 400$

$x = \sqrt{400}$

$x = 20ft$

Therefore the ladder is 20 ft up the wall.

Answer 2

Answer: 20 feet.

Step-by-step explanation:

Observe the right triangle attached.

You need to find the value of "x".

Then, you can use the Pythagorean Theorem:

$a^2=b^2+c^2$

Where "a" is the hypotenuse of the triangle, and "b" and "c" are the legs.

 In this case, you can identify that:

$a=25ft\\b=15ft\\c=x$

Substitute these values into  $a^2=b^2+c^2$:

 $(25ft)^2=(15ft)^2+x^2$

Now, you need to solve for x to find how far up the wall the top of the ladder reaches. Then you get:

$x^2=(25ft)^2-(15ft)^2$

$x=\sqrt{(25ft)^2-(15ft)^2}$

$x=20ft$