Given:
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.
Length of BD:
The length of BD can be determined by substituting the coordinates (-2,3) and (2,6) in the formula,
[tex]BD=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]BD=\sqrt{(2+2)^2+(6-3)^2}[/tex]
[tex]BD=\sqrt{(4)^2+(3)^2}[/tex]
[tex]BD=\sqrt{16+9}[/tex]
[tex]BD=\sqrt{25}[/tex]
[tex]BD=5[/tex]
Length of DE:
Substituting the coordinates of D(2,6) and E(3,2) in the formula, we get;
[tex]DE=\sqrt{(3-2)^2+(2-6)^2}[/tex]
[tex]DE=\sqrt{(1)^2+(-4)^2}[/tex]
[tex]DE=\sqrt{1+16}[/tex]
[tex]DE=\sqrt{17}[/tex]
Length of BE:
Substituting the coordinates of B(-2,3) and E(3,2) in the formula, we get;
[tex]BE=\sqrt{(3+2)^2+(2-3)^2}[/tex]
[tex]BE=\sqrt{(5)^2+(-1)^2}[/tex]
[tex]BE=\sqrt{25+1}[/tex]
[tex]BE=\sqrt{26}[/tex]
Perimeter of ΔBDE:
The perimeter of triangle BDE can be determined by adding the lengths of BD, DE and BE.
Thus, we have;
[tex]Perimeter=5+\sqrt{17}+\sqrt{26}[/tex]
Hence, the perimeter of ΔBDE is √17 + √26 + 5
Thus, Option A is the correct answer.
