NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 6: Triangles - Exercise 6.2
Question 7

Question. 7

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

Answer:

Yes.

Video Explanation:

Detailed Answer with Explanation:

Step 1: Let the smaller triangle have sides \(x, y, z\).

Step 2: Then, according to the question, the larger triangle will have:

  • First side = \(3x\)
  • Second side = \(3y\)
  • Perimeter = \(3(x + y + z)\)

Step 3: The perimeter of the larger triangle is the sum of its three sides. So, \(3x + 3y + \text{third side} = 3(x + y + z)\).

Step 4: Simplify:

\(3x + 3y + \text{third side} = 3x + 3y + 3z\).

Therefore, the third side = \(3z\).

Step 5: Now the sides of the larger triangle are \(3x, 3y, 3z\).

Step 6: Compare the sides of the two triangles:

\(\dfrac{3x}{x} = \dfrac{3y}{y} = \dfrac{3z}{z} = 3\).

Step 7: Since all three pairs of corresponding sides are in the same ratio, the two triangles are similar by the SSS (Side-Side-Side) similarity criterion.

Open NCERT PDFOpen NCERT Answers PDF