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Two sides and the perimeter of one triangle are respectively three times the corresponding sides and the perimeter of the other triangle. Are the two triangles similar? Why

Solution:

Given, the two sides and the perimeter of one triangle are three times the corresponding sides and the perimeter of the other triangle.

perimeter

We have to determine if the two triangles are similar.

The perimeter of a triangle is the sum of all three sides of a triangle.

Let us consider the first triangle be ABC and the second triangle be PQR

The sides of the first triangle ABC are x, y, and z.

So, the sides of the second triangle PQR will be 3x, 3y and 3z.

Perimeter of the triangle ABC = x + y + z

Perimeter of the triangle PQR = 3x + 3y + 3z = 3(x + y + z)

It is obvious that the sides are increased by a factor 3.

The SSS similarity criterion states that if the three sides of one triangle are proportional to the three sides of another, then the two triangles are similar.

Here, the perimeter and the two sides of a triangle are in proportion.

So, the third side will also be proportional.

Therefore, the two triangles are similar.

✦ Try This: Two sides and the perimeter of one triangle are respectively two times the corresponding sides and the perimeter of the other triangle. Are the two triangles similar? Why?

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 6

NCERT Exemplar Class 10 Maths Exercise 6.2 Problem 7

Two sides and the perimeter of one triangle are respectively three times the corresponding sides and the perimeter of the other triangle. Are the two triangles similar? Why?

Summary:

Two sides and the perimeter of one triangle are respectively three times the corresponding sides and the perimeter of the other triangle. The two triangles are similar as the two sides and the perimeter are in proportion, then the third sides will also be in proportion.

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