Question

the ratio of the corresponding sides of two similar triangle is4:5 then the ratio of their corresponding areas​

Answer 1

$\huge\bigstar\underline\mathfrak\red{Answer-}$

If the ratio of the corresponding sides of two similar triangle is 4:5, then the ratio of their corresponding areas is $\frac{16}{25}$ .

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$\huge\bigstar\underline\mathfrak\red{Explanation-}$

Given :

• ∆ABC ~ ∆DEF
• Ratio of corresponding sides of ∆s is 4:5.

To find :

• Ratio of areas of both similar ∆s.

Solution :

According to area theorem, "The ratio of the areas of two similar ∆s is equal to the square of their corresponding sides."

=> $\frac{area\:of\:triangle\:ABC}{area\:of\:triangle\:DEF} = ( { \frac{4}{5} )}^{2}$

=> $\frac{area \: of \: triangle \: ABC}{area \: of \: triangle \: DEF} = \frac{16}{25}$

$\therefore$ If the ratio of the corresponding sides of two similar triangle is 4:5, then the ratio of their corresponding areas is $\frac{16}{25}$ .

Answer 2

Answer:

The required ratio is $\dfrac{16}{25}$

Step-by-step explanation:

Given -

The ratio of the corresponding sides of two similar triangle is 4:5

∆ABC ~ ∆DEF

To Find -

The ratio of their corresponding areas​.

Solution :

As given,

The ratio of the corresponding sides of two similar triangle is 4:5

So,

We know that :

Area Theorem.

Statement :

The ratio of areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Now,

According to the Theorem,

$\sf\\ \\\implies \dfrac{\s {Area\;of \;\triangle\;ABC}}{{Area\;of\;\triangle\;FDE}}}$

$\sf \\ \\\implies \left({\dfrac{4}{5}\right)}^{2}$

$\sf\\ \\\implies \dfrac{16}{25}$

Therefore,

The required ratio is $\dfrac{16}{25}$