NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 7: Coordinate Geometry - Exercise 7.1

Question 6

Step 1: The given vertices of the triangle are:

• Point A = \((0,4)\)
• Point B = \((0,0)\)
• Point C = \((3,0)\)

Step 2: Use the distance formula to find the length of each side.

The distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is:

\(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

Step 3: Find side AB.

\(A(0,4), B(0,0)\)

\(AB = \sqrt{(0-0)^2 + (0-4)^2} = \sqrt{0 + 16} = 4\,\text{units}\)

Step 4: Find side BC.

\(B(0,0), C(3,0)\)

\(BC = \sqrt{(3-0)^2 + (0-0)^2} = \sqrt{9 + 0} = 3\,\text{units}\)

Step 5: Find side AC.

\(A(0,4), C(3,0)\)

\(AC = \sqrt{(3-0)^2 + (0-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5\,\text{units}\)

Step 6: Add all the three sides to get the perimeter.

Perimeter = AB + BC + AC = \(4 + 3 + 5 = 12\,\text{units}\)

Final Answer: The perimeter of the triangle is 12 units.