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?

Question

asked Sep 26, 2020 50.8k views

2 Answers

Cadavre · Answer 1 · 2020-09-27T22:23:46+0000

Answer: 20 feet.

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=√((25ft)^2-(15ft)^2)

x=20ft

Ed Sykes · Answer 2 · 2020-10-03T07:52:31+0000

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 = √(400)

x = 20ft

Therefore the ladder is 20 ft up the wall.