Question

If ∆ABC ~ ∆DEF and EF = 1/3 BC , then ar(∆ABC) : ar(∆ABC) ar(∆DEF) is

Answer 1

Answer:

area of ∆ABC is 9 times the area of ∆DEF

Step-by-step explanation:

(EF/BC)^2=area of ∆DEF/area of∆ABC

(1/3)^2=area of ∆DEF/area of∆ABC

1/9=area of ∆DEF/area of ∆ABC

area of ∆ABC/area of ∆DEF=9/1

in this the property of similar triangle has been applied.

I hope this may help you

Answer 2

Given:

∆ABC ~ ∆DEF

EF=1/3×BC

To find:

ar(∆ABC):ar(∆DEF)

Solution:

We can find the ratio by following the steps given below-

We know that in similar triangles, the ratio of areas is equal to the ratio of the square of corresponding sides of triangles.

EF=1/3×BC

EF/BC=1/3

EF²/BC²=1²/3²

(EF/BC)²=1/9

The ratio of areas of triangles= ar(∆ABC):ar(∆DEF)

ar(∆ABC):ar(∆DEF)= (EF/BC)²

ar(∆ABC)/ar(∆DEF)=1/9

Therefore, ar(∆ABC):ar(∆DEF) is 1:9.