Two ladders are leaning against a wall at the same angle, as shown. How long is the short ladder?
the long ladder is 50ft and 60ft the short ladder is 20ft
my answer choices r 20 ft 24 ft 30 ft and 40 ft
i think its 30
as shown ------ not
If you say that you have 2 ladders, then
"the long ladder is 50ft and 60ft the short ladder is 20ft"
is a gibberish statement.
soo uhh what is it?
To determine the length of the short ladder, we can use the concept of similar triangles. Since the two ladders are leaning against the wall at the same angle, the triangles formed by the ground, the wall, and each ladder are similar.
Let's call the length of the short ladder "x."
Using the property of similar triangles, we can set up a proportion:
(long ladder length) / (short ladder length) = (long ladder height) / (short ladder height)
Plugging in the known values:
60ft / x = 50ft / 20ft
To solve for x, we can cross multiply and then divide:
60ft * 20ft = 50ft * x
1200ft² = 50ft * x
Now, divide both sides of the equation by 50ft to isolate x:
(1200ft²) / 50ft = x
24ft = x
Therefore, the length of the short ladder is 24 ft.