Question

A triangle has sides of lengths 20, 28, and 32. A similiar triangle has a side of length 15 and another of length 24. How long is the third side of this triangle?

Answer 1

for similar triangles, the ratio of the sides of the first triangle is equal to the ration of the corresponding sides of the second triangle,, like:
let h1 = height of 1st triangle
let h2 = height of 2nd triangle
let b1 = base of 1st triangle
let b2 = base of 2nd triangle
therefore, if they are similar triangles,
(h1)/(b1) = (h2)/(b2)

thus in the question, we can write:
let x = third side
20/15 = 32/24 = 28/x
simplifying:
4/3 = 28/x
solving for the third side,
x = 21

hope this helps~ :)

Answer 2

20/15 = 4/3

28/24 = nope
32/24 = 4/3 yes

so
20 --> 15
32 --> 24
28(3/4) = 21

so
20 , 28 , 32
--->
15 , 21 , 24