QuestionSeptember 19, 2025

Find the perimeter of the triangle with these vertices. (4,3),(-3,3),(-3,-3) Give an exact answer (not a decimal approximation). Simplify your answer as much as possible.

Find the perimeter of the triangle with these vertices. (4,3),(-3,3),(-3,-3) Give an exact answer (not a decimal approximation). Simplify your answer as much as possible.
Find the perimeter of the triangle with these vertices. (4,3),(-3,3),(-3,-3) Give an exact answer (not a decimal approximation). Simplify your answer as much as possible.

Solution
4.2(235 votes)

Answer

13 + \sqrt{85} Explanation 1. Find side lengths using distance formula Use d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} for each pair. - Between (4,3) and (-3,3): d_1 = \sqrt{(4+3)^2 + (3-3)^2} = \sqrt{49} = 7 - Between (-3,3) and (-3,-3): d_2 = \sqrt{(-3+3)^2 + (3+3)^2} = \sqrt{36} = 6 - Between (-3,-3) and (4,3): d_3 = \sqrt{(4+3)^2 + (3+3)^2} = \sqrt{49+36} = \sqrt{85} 2. Add the side lengths Perimeter = d_1 + d_2 + d_3 = 7 + 6 + \sqrt{85}

Explanation

1. Find side lengths using distance formula<br /> Use $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ for each pair.<br />- Between $(4,3)$ and $(-3,3)$: $d_1 = \sqrt{(4+3)^2 + (3-3)^2} = \sqrt{49} = 7$<br />- Between $(-3,3)$ and $(-3,-3)$: $d_2 = \sqrt{(-3+3)^2 + (3+3)^2} = \sqrt{36} = 6$<br />- Between $(-3,-3)$ and $(4,3)$: $d_3 = \sqrt{(4+3)^2 + (3+3)^2} = \sqrt{49+36} = \sqrt{85}$<br /><br />2. Add the side lengths<br /> Perimeter $= d_1 + d_2 + d_3 = 7 + 6 + \sqrt{85}$
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