Question

the ratio of corresponding sides of similar triangles is 4:5. Find the ratios of their areas. (STD 10).​

Answer 1

Answer:

we know that the ratio of the area of two similar triangle is equal to the ratio of the square of the corresponding sides.

ratio of area= (4)^2:(5)^2

= 16:25

Answer 2

$\large\bf\underline {To \: find:-}$

• we need to find the ratio of areas

$\large\bf\underline{Given:-}$

• ratio of sides of similar triangles is 4:5

⚘$\huge\bf\underline{Solution:-}$

Let the ratio of sides of two similar triangles be

S1:S2 = 4:5

It is given in the Question that the two triangles are similar.

As we know that,

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

So,

Let the Ratio of areas of two similar triangles be A1 :A2.

$\rm \dashrightarrow\large \: \frac{A1}{A2} = (\frac{S1}{S2} ) {}^{2}$

$\rm \dashrightarrow\large \: \frac{A1}{A2} = (\frac{4}{5}) {}^{2}$

$\rm \dashrightarrow\large \: \frac{A1}{A2} = \frac{16}{25}$

hence,

❥ Ratio of areas of two similar triangles is 16:25

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