Question

The area of similar triangle are 729 cm² and 576 cm² respectively.find the ratio of their corresponding sides​

Answer 1

Given :

• The area of similar triangle are 729 cm² and 576 cm² respectively.

To Find :

• The ratio of the measures of their corresponding sides.

Solution :

The ratio of the corresponding sides of the given similar triangles will be the ratio of the areas of the similar triangles.

Forming a ratio from the area :-

→ 729 : 576

Dividing both the terms by 3 :-

→ 243 : 192

Dividing again by 3 :-

→ 81 : 64

There are no other common factors to 81 and 64.

Therefore the ratio of the corresponding sides of the given similar triangles is 81 : 64.

Extra Information :-

TRIANGLES :

A triangle is the simplest polygon with only three sides. The sum of all the angles of a triangle is 180 degrees. When two triangles are said to be similar, it means that the ratio of the corresponding sides of these triangles is equal to the ratio of the areas.

Answer 2

Final Answer:

The ratio of the corresponding sides of the similar triangles, which have the values of the area  $729 cm^2$ and $576 cm^2$ respectively, is 9:8.

Given:

The areas of the similar triangles are $729 cm^2$ and $576 cm^2$ respectively. ​

To Find:

The ratio of the corresponding sides of the similar triangles, which has the values of the area  $729 cm^2$ and $576 cm^2$ respectively. ​

Explanation:

Similar triangles are those triangles, which have their respective angles, and sides proportional to each other.

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

Step 1 of 2

As per the statement in the given problem, write the following equation.

The ratio of the areas of similar triangles is

$=\frac{729}{576} \\\\=\frac{729\div 9}{576\div 9} \\\\=\frac{81}{64} \\\\=\frac{9^2}{8^2}$

Step 2 of 2

In accordance with the above calculations, deduce the following.

The ratio of the corresponding sides of similar triangles is equal to the square root of the ratio of the areas of similar triangles, which is:

$=\frac{\sqrt{9^2}}{\sqrt{8^2}}\\=\frac{9}{8}$

Therefore, the required ratio of the corresponding sides of the similar triangles, which have the values of the area  $729 cm^2$ and $576 cm^2$ respectively, is 9:8.

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