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The triangle in the figure has vertices at points P(0, 0), Q(0, 6.5), and R(3, 2).  What is the perimeter of the triangle?

Question

The triangle in the figure has vertices at points P(0, 0), Q(0, 6.5), and R(3, 2).  What is the perimeter of the triangle?

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Solution

To find the perimeter of the triangle, we need to find the length of all three sides and add them together.

  1. The length of side PQ can be found using the distance formula, or simply by subtracting the y-coordinates since the x-coordinates are the same. So, PQ = 6.5 - 0 = 6.5 units.

  2. The length of side PR can be found using the Pythagorean theorem since this is a right triangle (one point is at the origin). So, PR = sqrt((3-0)^2 + (2-0)^2) = sqrt(9 + 4) = sqrt(13) units.

  3. The length of side QR can also be found using the Pythagorean theorem. So, QR = sqrt((3-0)^2 + (6.5-2)^2) = sqrt(9 + 20.25) = sqrt(29.25) units.

Finally, add up all three sides to get the perimeter: 6.5 + sqrt(13) + sqrt(29.25) units.

This problem has been solved

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