Question

The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is ______.

विकल्प

• 5 units

• 12 units

• 10 units

• 11 units

• `7 + sqrt(5)` units

Answer 1

The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is 12 units.

Explanation:

The vertices of a triangle are (0, 4), (0, 0) and (3, 0).

Now, perimeter of ΔAOB = Sum of the length of all its sides

= Distance between (OA + OB + AB)

Distance between the points (x₁, y₁) and (x₂, y₂) is given by,

d = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`

To find:

Distance between A(0, 4) and O(0, 0) + Distance between O(0, 0) and B(3, 0) + Distance between A(0, 4) and B(3, 0)

= `sqrt((0 - 0)^2 + (0 - 4)^2) + sqrt((3 - 0)^2 + (0 - 0)^2) + sqrt((3 - 0)^2 + (0 - 4)^2)`

= `sqrt(0 + 16) + sqrt(9 + 0) + sqrt((3)^2 + (4)^2`

= `4 + 3 + sqrt(9 + 16)`

= `7 + sqrt(25)`

= 7 + 5

= 12

Therefore, the required perimeter of the triangle is 12.