Question

Find the probability that a point chosen at random inside the large triangle is in the small triangle.
https://cds.flipswitch.com/tools/asset/media/87793

Answer 1

find the area of both triangles

Answer 2

it might be useful to know that any linear scale translates into a squared scale when it comes to area

for example: a 2x2 square has linear sides of 2, and an area of 4

if we scale it by 3; the sides become 3(2), and the area is therefore 3(2)*3(2),
or just 3^2 (4)

Answer 3

15k = 4, when k=4/15, so our linear scale is 4/15 to work with in this case

Answer 4

lets spose we wanted to work the ratio of the example on squares ...

6k = 2, when k=2/6 = 1/3

k^2 = 1/9
--------------------

now the areas of our square example is 36 and 4: 4/36 = 1/9 .... so what can we conject from this?

Answer 5

lets see if the shape matters

the area of the larger is 15h/2 for whatever the height is

the area of the smaller is 15(4/15) * h(4/15)/2

\[\frac{15h(4/15)^2/~2}{15h/2}\]
\[\frac{15h(4/15)^2}{15h}\]
\[\frac{h(4/15)^2}{h}\]
\[\frac{(4/15)^2}{1}\]
doesnt seem to matter what shape it is, as long as they are similar shapes :)