Question

If $\triangle ABC and \triangle DEF$ are two triangles such that $\frac {AB}{DE} = \frac {BC}{EF} = \frac {CA}{FD}= \frac {2}{5}$, then Area ($\triangle ABC$) : Area ($\triangle DEF$ ) =
(a) 2 : 5
(b) 4 : 25
(c) 4 : 15
(d) 8 : 125

Answer 1

Answer:

The ratio of Area (ΔABC) : Area (ΔDEF) is 4 : 25

Among the given options option (b) is 4 : 25 is the correct answer.

Step-by-step explanation:

Given :

In ΔABC and ΔDEF  

AB/DE = BC/EF = CA/FD  = 2/5

 ΔABC ~ ΔDEF

[Two triangles are said to be similar, if their corresponding sides are proportional]

 

ar (ΔABC) / ar(ΔDEF) = AB²/DE²

[The ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides]

ar (ΔABC) / ar(ΔDEF) = 2²/5²

ar (ΔABC) / ar(ΔDEF) = 4/25

ar (ΔABC) : ar(ΔDEF) = 4 : 25

Hence, the ratio of ar (ΔABC) : ar(ΔDEF) is 4 : 25

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Answer 2

Solution:

We have been given two triangles ∆ABC and ∆DEF such that $\frac {AB}{DE} = \frac {BC}{EF} = \frac {CA}{FD}= \frac {2}{5}$.

So, ∆ABC and ∆ DEF are similar because Two triangles are considered to be similar,if their corresponding Sides equal to each other.

∴ ∆ ABC ∼ ∆ DEF

We have to find the ratio of area ∆ABC to area ∆DEF.

0r, ar(∆ABC) / ar(∆ABC) = AB²/DE²

0r, ar(∆ABC) / ar(∆ABC) = 2²/5²

0r, ar(∆ABC) / ar(∆ABC) = 4/25

0r, ar(∆ABC) : ar(∆ABC) = 4 : 25

Therefore, ar(∆ABC) : ar(∆DEF) = 4 : 25