If the scale factor of two similar solids is 3 : 10, what is the ratio of their corresponding areas and volumes? ratio of area 100:9; ratio of volumes 1000:27
ratio of area 9:100; ratio of volumes 27:1000
ratio of area 3:10; ratio of volume 9:100
ratio of area 10:3; ratio of volume 100:9

isocolese triangle

we know that the line connect a and b is the hyptonuse

so first find the hypotonuse length using the distance formula, call the length c

since it is an isocolese triangle, the lengths of the legs are the same

using pythagorean theorem,

in this case, a=b since isocolese triangle so we get

or

we can find c so we can find the distances

we know that if we draw 2 circles, each has center at a and b, and find where they intersect, we can the 2 possible locations for c

if a has center at (xa,ya) and b has center at (xb,yb), then we can solve where

and

intersect to find where they intersect

i'm not going to put an example because i have to go to class. i hope this explanation is enough