<u>Given</u>:
Given that the graph of a triangle BDE.
The coordinates of the triangle are B(-2,3), D(2,6) and E(3,2)
We need to determine the perimeter of the triangle BDE.
<u>Length of BD:</u>
The length of BD can be determined by substituting the coordinates (-2,3) and (2,6) in the formula,
![BD=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=BD%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
![BD=\sqrt{(2+2)^2+(6-3)^2}](https://tex.z-dn.net/?f=BD%3D%5Csqrt%7B%282%2B2%29%5E2%2B%286-3%29%5E2%7D)
![BD=\sqrt{(4)^2+(3)^2}](https://tex.z-dn.net/?f=BD%3D%5Csqrt%7B%284%29%5E2%2B%283%29%5E2%7D)
![BD=\sqrt{16+9}](https://tex.z-dn.net/?f=BD%3D%5Csqrt%7B16%2B9%7D)
![BD=\sqrt{25}](https://tex.z-dn.net/?f=BD%3D%5Csqrt%7B25%7D)
![BD=5](https://tex.z-dn.net/?f=BD%3D5)
<u>Length of DE:</u>
Substituting the coordinates of D(2,6) and E(3,2) in the formula, we get;
![DE=\sqrt{(3-2)^2+(2-6)^2}](https://tex.z-dn.net/?f=DE%3D%5Csqrt%7B%283-2%29%5E2%2B%282-6%29%5E2%7D)
![DE=\sqrt{(1)^2+(-4)^2}](https://tex.z-dn.net/?f=DE%3D%5Csqrt%7B%281%29%5E2%2B%28-4%29%5E2%7D)
![DE=\sqrt{1+16}](https://tex.z-dn.net/?f=DE%3D%5Csqrt%7B1%2B16%7D)
![DE=\sqrt{17}](https://tex.z-dn.net/?f=DE%3D%5Csqrt%7B17%7D)
<u>Length of BE:</u>
Substituting the coordinates of B(-2,3) and E(3,2) in the formula, we get;
![BE=\sqrt{(3+2)^2+(2-3)^2}](https://tex.z-dn.net/?f=BE%3D%5Csqrt%7B%283%2B2%29%5E2%2B%282-3%29%5E2%7D)
![BE=\sqrt{(5)^2+(-1)^2}](https://tex.z-dn.net/?f=BE%3D%5Csqrt%7B%285%29%5E2%2B%28-1%29%5E2%7D)
![BE=\sqrt{25+1}](https://tex.z-dn.net/?f=BE%3D%5Csqrt%7B25%2B1%7D)
![BE=\sqrt{26}](https://tex.z-dn.net/?f=BE%3D%5Csqrt%7B26%7D)
<u>Perimeter of ΔBDE:</u>
The perimeter of triangle BDE can be determined by adding the lengths of BD, DE and BE.
Thus, we have;
![Perimeter=5+\sqrt{17}+\sqrt{26}](https://tex.z-dn.net/?f=Perimeter%3D5%2B%5Csqrt%7B17%7D%2B%5Csqrt%7B26%7D)
Hence, the perimeter of ΔBDE is √17 + √26 + 5
Thus, Option A is the correct answer.