Question

two similar triangles have areas 120 square cm and 480 square CM respectively then the ratio of any pair of corresponding side is​

Answer 1

Step-by-step explanation:

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

See the attachment for answer.

I hope it will help you

Answer 2

The ratio of any pair of their corresponding side is​ 1:2.

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Let's understand a few concepts:

To find Area (triangle STU) we must use the Theorem of Areas of Similar Triangles.

What are similar triangles?

Two triangles are said to be similar if their corresponding angles are equal and their corresponding sides are proportional to each other.

What is the Theorem of Areas of Similar Triangles?

The theorem states that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

For example: if ΔABC and ΔPQR are two similar triangles then we can say that,

$\boxed{\bold{\frac{Area(\triangle ABC)}{Area(\triangle PQR)} = \bigg(\frac{AB}{PQ}\bigg)^2 = \bigg(\frac{BC}{QR}\bigg)^2 = \bigg(\frac{AC }{PR}\bigg)^2 }}$

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Let's solve the given problem:

Let's say the two similar triangles are Δ ABC and Δ PQR and we will find the ratio of their corresponding sides AB and PQ respectively.

So, here we have

Area (Δ ABC) = 120 cm²

Area (Δ PQR) = 480 cm²

By using the above theorem of the areas of similar triangles, we get

$\frac{Area(\triangle ABC)}{Area(\triangle PQR)} = \bigg(\frac{AB}{PQ}\bigg)^2$

• on substituting the given values

$\implies \frac{120\:cm^2}{480\:cm^2} = \bigg(\frac{AB}{PQ}\bigg)^2$

• taking square root on both sides

$\implies \sqrt{\frac{120\:cm^2}{480\:cm^2}} = \sqrt{\bigg(\frac{AB}{PQ}\bigg)^2}$

$\implies \sqrt{\frac{1}{4}} = \sqrt{\bigg(\frac{AB}{PQ}\bigg)^2}$

• 1² = 1 and 2² = 4

$\implies \sqrt{\frac{1}{(2)^2}} = \sqrt{\bigg(\frac{AB}{PQ}\bigg)^2}$

$\implies \frac{AB}{PQ} = \frac{1}{2}$

$Similarly, \:\bold{AB : PQ = BC : QR = AC : PR= 1: 2}$

Thus, the ratio of any pair of the corresponding side is 1 : 2.

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