Question

What is the similarity ratio of ΔABC to ΔDEF?
Tri ABC: AC=4 CB=5
Tri DEF: DF= 2

Answer 1

The similarity ratio of ΔABC to ΔDEF = 2 : 1.

Solution:

The image attached below.

Given  ΔABC to ΔDEF are similar.

To find the ratio of similarity triangle ABC and triangle DEF.

In ΔABC: AC = 4 and CB = 5

In ΔDEF: DF = 2, EF = ?

Let us first find the length of EF.

We know that, If two triangles are similar, then the corresponding sides are proportional.

⇒ $\frac{AC}{DF} =\frac{BC}{EF}$

⇒ $\frac{4}{2} =\frac{5}{EF}$

⇒ $4EF=5\times2$

⇒ $EF=\frac{5\times 2}{4}$

⇒ $EF=\frac{5}{2}$

Ratio of ΔABC to ΔDEF = $\frac{AC}{DF} =\frac{4}{2}=\frac{2}{1}$

Similarly, ratio of ΔABC to ΔDEF = $\frac{BC}{EF} =\frac{5}{\frac{5}{2}}=\frac{2}{1}$

Hence, the similarity ratio of ΔABC to ΔDEF = 2 : 1.