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

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Detailed Solution

The perimeter of a triangle with vertices

0, 4, (0, 0)

and (3, 0) is 12.
Triangle co-ordinates are given as (0,4), (0,0), (3,0).
Let us draw the figure.
Question Image

We can calculate by using the distance formula which is

d = \sqrt{{(y_{2} - y_{1})}^{2} + {(x_{2} - x_{1})}^{2}}

.
AB=

\sqrt{{(0 - 4)}^{2} + {(3 - 0)}^{2}}

\Rightarrow AB = 5 units

OB=

\sqrt{{(0 - 0)}^{2} + {(3 - 0)}^{2}}

\Rightarrow OB = 3 units

OA=

\sqrt{{(4 - 0)}^{2} + {(0 - 0)}^{2}}

\Rightarrow OA = 4 units

The length of the sides is 4, 3, 5 respectively.
Perimeter of a triangle is its total boundary length.
Perimeter= 4+3+5=12.
The perimeter is 12 units.

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