Question

The perimeter of the triangle with vertical (0,0) , (3,0) and (0,3) is

Answer 1

A(0, 0), B(3, 0), C(0, 3) are the vertices of triangle ABC.
Perimeter of triangle ABC = AB + BC + AC
Using Distance Formula,
AB
$= \sqrt{ {( x_{1} - x_{2})}^{2} + {( y_{1} - y_{2})}^{2} }$
$= \sqrt{ {(0 - 3 ) }^{2} + {(0 - 0)}^{2} }$
$= \sqrt{ {( - 3)}^{2} + {(0)}^{2} }$
$= \sqrt{9}$
$= 3$
Similarily,
BC
$= \sqrt{ {(3 - 0)}^{2} + {(0 - 3)}^{2} }$
$= \sqrt{ {(3)}^{2} + {( - 3)}^{2} }$
$= \sqrt{9 + 9}$
$= \sqrt{18}$
$= \sqrt{2 \times 9}$
$= 3 \sqrt{2}$
CA
$= \sqrt{ {(0 - 0)}^{2} + {(0 - 3)}^{2} }$
$= \sqrt{ {(0)}^{2} + {( - 3)}^{2} }$
$= \sqrt{0 + 9}$
$= \sqrt{9}$
$= 3$
Perimeter = AB + BC + CA
$= 3 + 3 \sqrt{2} + 3$
$= 6 + 3 \sqrt{2}$
$= 6 + 3 \times 1.41$
$= 6 + 4.23$
$= 10.23$
Hence, the perimeter of the triangle = 10.23 units.

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