Question

ΔABC and ΔDEF are similar and AB = 1/3



DE, then find ar(ΔABC) : ar(ΔDEF).​

Answer 1

Answer:

Given :-

ABC and DEF are two similar △'s.

AB = DE

To find:-

ar (△ABC) : ar (△DEF)

Solution:-

Since, △ABC and △DEF are two similar triangles.(Given)

We know that,

The ratio of the areas of the two similar triangles is equal to the ratio of the squares of their corresponding sides. (Theorem)

By using this theorem,

We have, AB = 1/3 DE

DE = 3AB ; put Value of DE

then,

cancel out AB².

hence, the ratio of the area of △ABC and △DEF is 1 : 9 .

Step-by-step explanation:

Answer 2

Answer:

your answer is

ar (∆ABC) : ar (∆DEF) =1:9

Given =

ABC and DEF are two similar triangles

AB= 1/3 DE

To prove that = ar (∆ABC ) : ar (∆DEF)

proof =

since ∆ ABC and ∆ DEF are two similar triangles (Given)

we know that ,

The ratio of the areas of the two similar triangles is equal to the ratio of the squares of the corresponding sides ( according to theorem)

by using this theorem

ar (ABC). = AB 2

ar (DEF). DE 2

we have Ab=1/3 DE

DE =3 AB, put the value of DE

then,

ar (ABC) . = AB 2

ar (DEF). (3AB)

ar (ABC). = AB 2

ar (DEF). 9AB 2

cancel AB 2 ( AB square)

ar (ABC) . = 1

ar (DEF). 9

Hence the ratio of the area of ∆ABC and ∆DEF is . 1:9

hope this helps u ☺️✌