Question

∆ ABC ~ ∆ DEF, the A(∆ABC) :A(∆DEF) = 49 :100. FIND THE RATIO OF AB:DE.

Answer 1

Step-by-step explanation:

this is the answer☝️☝️

7:10

Answer 2

Given:

∆ ABC ~ ∆ DEF

A(∆ABC) :A(∆DEF)=49 :100

To find:

The ratio of AB and DE

Solution:

The ratio of AB and DE is 7:10.

We will calculate the ratio by following the given steps-

It is mentioned that the triangles DEF and ABC are similar.

So, taking the ratio of the Ar(∆ABC) and Ar(∆DEF), we see that it is equal to the ratio obtained on dividing the corresponding sides' squares.

In ∆ DEF and ∆ ABC, the sides corresponding to one another are equal as they are similar.

AB/DE=BC/EF=AC/DF

We are given that on dividing the areas of triangles DEF and ABC, we get 49/ 100.

A(∆ABC) :A(∆DEF)=49: 100

A(∆ABC)/ A(∆DEF)=$(AB/DE)^{2}$

49/100=$(AB/DE)^{2}$

$(7/10)^{2}$=$(AB/DE)^{2}$

7/10=AB/DE

So, AB: DE=7: 10.

Thus, the ratio of AB and DE is 7:10.