the triangles formed by two ladders leaning against a wall are similar. how long is the shorter ladder?

the first ladder is 42ft and leans against the wall at 24ft, and the shorter ladder leans against the wall at 8ft.

Amazing work

What’s the answer ?

18 To find the length of the shorter ladder, we can use the concept of similar triangles.

Similar triangles have proportional sides. In this case, we have two triangles: one formed by the shorter ladder leaning against the wall, and another formed by the longer ladder leaning against the wall.

Let's denote the length of the shorter ladder as x. According to the given information, the longer ladder is 42ft in length and leans against the wall at 24ft.

Based on the similarity of the two triangles, we can set up the following proportion:

x/8 = 42/24

To solve for x, we can cross-multiply:

24x = 8 * 42

Now, divide both sides of the equation by 24:

x = (8 * 42) / 24

Simplifying further:

x = 336 / 24

x = 14

Therefore, the length of the shorter ladder is 14 feet.

just use a proportion

x/8 = 42/24 = 7/4
4x = 56

carry on...