Question

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?

Answer 1

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?

Answer 2

Answer:

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

$\frac{Area(ABC)}{Area(DE F)}=\frac{(x)^2}{(3x)^2}$

$\frac{1}{Area(DE F)}=\frac{(x)^2}{9(x)^2}$

Cancel out the common factors.

$\frac{1}{Area(DE F)}=\frac{1}{9}$

On cross multiplication, we get

$1\times 9=1\times Area(DE F)}$

$9=Area(DE F)}$

Therefore the area of triangle DEF is 9 square units.