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Distance Formula

Find the peri...

Question

Find the perimeter of the triangle with vertices $(- 2, 3), (4, 3),$ and $(6, - 3)$ .

4 \sqrt{11}

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18 \sqrt{10}

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10 + 4 \sqrt{5}

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16 + 2 \sqrt{10}

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16 + 3 \sqrt{7}

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Solution

The correct option is D $16 + 2 \sqrt{10}$
For perimeter, we have to find length of each side of triangle.
The distance between $(- 2, 3)$ and $(4, 3)$ is $\sqrt{36} = 6$
The distance between $(- 2, 3)$ and $(6, - 3)$ is $\sqrt{64 + 36} = 10$
The distance between $(4, 3)$ and $(6, - 3)$ is $\sqrt{4 + 36} = 2 \sqrt{10}$
$∴$ perimeter is $6 + 10 + 2 \sqrt{10} = 16 + 2 \sqrt{10}$ .

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