Triangles abc and def are similar. the ratio of the side lengths in triangle abc to triangle def is 1: 3. if the area of triangle abc is 1 square unit, what is the area of triangle def?

The area of triangle DEF is 9 square units.

Step-by-step explanation:

It is given that triangle ABC and DEF are similar and the ratio of the side lengths in triangle ABC to triangle DEF is 1:3.

Let the length of their sides be x and x respectively.

If two triangles are similar then the ratio of their areas is equal to the square of the ratio of their sides.

Since triangle ABC and DEF are similar, therefore

Cancel out the common factors.

On cross multiplication, we get

Therefore the area of triangle DEF is 9 square units.

d. 8

step-by-step explanation:

the given radical expression is:

we can rewrite this as:

we express as square numbers to get;

the exponents will now cancel out to give.

the correct answer is d