To find the perimeter of triangle QRP with vertices Q(1, 6), R(-4, 2), and P(1, 2), we first need to compute the lengths of the sides QR, RP, and PQ using the distance formula:
The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
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Calculate the length of QR:
- \(Q(1, 6)\) and \(R(-4, 2)\) \[ QR = \sqrt{((-4) - 1)^2 + (2 - 6)^2} = \sqrt{(-5)^2 + (-4)^2} = \sqrt{25 + 16} = \sqrt{41} \]
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Calculate the length of RP:
- \(R(-4, 2)\) and \(P(1, 2)\) \[ RP = \sqrt{(1 - (-4))^2 + (2 - 2)^2} = \sqrt{(1 + 4)^2 + 0^2} = \sqrt{5^2} = 5 \]
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Calculate the length of PQ:
- \(P(1, 2)\) and \(Q(1, 6)\) \[ PQ = \sqrt{(1 - 1)^2 + (6 - 2)^2} = \sqrt{0^2 + 4^2} = \sqrt{16} = 4 \]
Now we can calculate the perimeter \(P\) of triangle QRP:
\[ \text{Perimeter} = QR + RP + PQ = \sqrt{41} + 5 + 4 \]
We need to compute \(\sqrt{41}\) to the nearest tenth:
\[ \sqrt{41} \approx 6.4 \]
So:
\[ \text{Perimeter} \approx 6.4 + 5 + 4 = 15.4 \]
Rounded to the nearest tenth, the perimeter of triangle QRP is:
\[ \boxed{15.4} \]