SOLUTION: Two triangles are similar.The length of a side of one of the triangles is 2 times that of corresponding sides of the other the area of the smaller triangle is 25cm².find the area o

Algebra ->  Triangles -> SOLUTION: Two triangles are similar.The length of a side of one of the triangles is 2 times that of corresponding sides of the other the area of the smaller triangle is 25cm².find the area o      Log On


   

Question 1105922: Two triangles are similar.The length of a side of one of the triangles is 2 times that of corresponding sides of the other the area of the smaller triangle is 25cm².find the area of the larger triangle.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
As you scale up a 2-dimensional shape by a factor of 2 ,
the area gets larger by a factor of 2%5E2=4 .
(It works that way for all shapes you are scaling up or down by any factor k%3E0 ,
to turn them into similar larger or smaller figures.
For 3-dimensional shapes, when you scale up or down by a factor k%3E0 ,
all corresponding surface areas change by a factork%5E2 ,
and the volume changes by k%5E3 ).
So, if the smaller figure has an area of 25cm%5E2 ,
the area of a similar figure with corresponding sides 2 times longer is
4%2A25cm%5E2=highlight%28100cm%5E2%29 .