Question

Pleaseeee helpppp me What is the perimeter of ABDE

Answer 1

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,

$BD=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$BD=\sqrt{(2+2)^2+(6-3)^2}$

$BD=\sqrt{(4)^2+(3)^2}$

$BD=\sqrt{16+9}$

$BD=\sqrt{25}$

$BD=5$

Length of DE:

Substituting the coordinates of D(2,6) and E(3,2) in the formula, we get;

$DE=\sqrt{(3-2)^2+(2-6)^2}$

$DE=\sqrt{(1)^2+(-4)^2}$

$DE=\sqrt{1+16}$

$DE=\sqrt{17}$

Length of BE:

Substituting the coordinates of B(-2,3) and E(3,2) in the formula, we get;

$BE=\sqrt{(3+2)^2+(2-3)^2}$

$BE=\sqrt{(5)^2+(-1)^2}$

$BE=\sqrt{25+1}$

$BE=\sqrt{26}$

Perimeter of ΔBDE:

The perimeter of triangle BDE can be determined by adding the lengths of BD, DE and BE.

Thus, we have;

$Perimeter=5+\sqrt{17}+\sqrt{26}$

Hence, the perimeter of ΔBDE is √17 + √26 + 5

Thus, Option A is the correct answer.