If ΔABC ~Δ DEF and ΔDEF has sides that are 3 times greater than those of ΔABC what is the relationship between the areas of the triangles? (Multiple Choice)

Question

If ΔABC ~Δ DEF and ΔDEF  has sides that are 3 times greater than those of ΔABC what is the relationship between the areas of the triangles? (Multiple Choice)

august899 · Answer

A.The area of  is 3 times greater than the area of ΔABC
 
 B. The area of  is 9 times greater than the area of ΔABC
 
 C. The area of  is 3 times greater than the area of ΔDEF
 
 D. The area of  is 9 times greater than the area of ΔDEF

hartnn · Answer

Area is proportional to square of sides.

for example, if sides are ratio 4:5,
then areas will be in the ratio 4^2 : 5^2 which is 16:25

hartnn · Answer

here, the sides of the triangles are in the ratio 1:3
so areas will be in the ratio?

august899 · Answer

So do I square the 3?

hartnn · Answer

yes

hartnn · Answer

1^2 : 3^2 = ..

august899 · Answer

Ok so that gets me 9. Is the answer B?

hartnn · Answer

yes :)

hartnn · Answer

A(ΔABC) : A(ΔDEF) = 1:9 

so, 
 The area of ΔDEF is 9 times greater than the area of ΔABC

august899 · Answer

Awesome! Thank you for the help!

hartnn · Answer

welcome ^_^