Question

What is the perimeter of DEFG?A, B, C or D​

Answer 1

Given:

Given that the figure DEFG with vertices D(1,2), E(2,6), F(6,7) and G(5,3)

We need to determine the perimeter of DEFG.

The length of the sides can be determined using the formula,

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

Length of DE:

Substituting the coordinates D(1,2), E(2,6) in the formula, we get;

$DE=\sqrt{(2-1)^2+(6-2)^2}$

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

$DE=\sqrt{17}$

Length of EF:

Substituting the coordinates E(2,6), F(6,7) in the formula, we get;

$EF=\sqrt{(6-2)^2+(7-6)^2}$

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

$EF=\sqrt{17}$

Length of FG:

Substituting the coordinates F(6,7), G(5,3) in the formula, we get;

$FG=\sqrt{(5-6)^2+(3-7)^2}$

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

$FG=\sqrt{17}$

Length of DG:

Substituting the coordinates D(1,2), G(5,3) in the formula, we get;

$DG=\sqrt{(5-1)^2+(3-2)^2}$

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

$DG=\sqrt{17}$

Perimeter of DEFG:

The perimeter of DEFG can be determined by adding the side lengths DE, EF, FG and DG.

Thus, we have;

$Perimeter=DE+EF+FG+DG$

Substituting the values, we have;

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

$Perimeter=4\sqrt{17}$

Thus, the perimeter of DEFG is 4√17

Hence, Option b is the correct answer.