Question

Find the perimeter of the triangle formed by points o(0,0) , (a,0) and (0,b).

Answer 1

it is a right angled triangle
distance between (0,0) and (a,0) = a

distance between (0,0) and (0,b)= b

using Pythagorean theorem
hypotenuse = root a^2+b^2

Answer 2

Answer:

$a+b+\sqrt{a^2+b^2}$

Step-by-step explanation:

A=(0,0)

B = (a,0)

C = (0,b)

Now find the sides of triangle AB,BC,AC

To find AB use distance formula :

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

$(x_1,y_1)=(0,0)$

$(x_2,y_2)= (a,0)$

Substitute the values in the formula :

$AB=\sqrt{(a-0)^2+(0-0)^2}$

$AB=\sqrt{(a)^2+(0)^2}$

$AB=\sqrt{a^2}$

$AB=a$

To Find BC

$(x_1,y_1)=(a,0)$

$(x_2,y_2)=(0,b)$

Substitute the values in the formula :

$BC=\sqrt{(0-a)^2+(b-0)^2}$

$BC=\sqrt{(-a)^2+(b)^2}$

$BC=\sqrt{a^2+b^2}$

To Find AC

$(x_1,y_1)=(0,0)$

$(x_2,y_2)=(0,b)$

Substitute the values in the formula :

$AC=\sqrt{(0-0)^2+(b-0)^2}$

$AC=\sqrt{(0)^2+(b)^2}$

$AC=\sqrt{b^2}$

$AC=b$

Thus the sides of the triangle are $a,b,\sqrt{a^2+b^2}$

Perimeter of triangle = Sum of all sides

                                  $a+b+\sqrt{a^2+b^2}$

Hence the perimeter of the triangle formed by points o(0,0) , (a,0) and (0,b) is  $a+b+\sqrt{a^2+b^2}$