Question

What is the perimeter of triangle DEF?

A 10.4 units
B 2.4 units
C 4.2 units
D. 12.2 units
HELP PlZ

Answer 1

Given:

Triangle DEF

To find:

The perimeter of triangle DEF.

Solution:

Coordinate of D = (-1, 1)

Coordinate of E = (2, 1)

Coordinate of F = (-1, 4)

Distance formula:

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

Distance of DE:

Here, $x_1=-1, y_1=1, x_2=2, y_2=1$

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

$d=\sqrt{0+9}$

d = 3 units

Distance of EF:

Here, $x_1=2, y_1=1, x_2=-1, y_2=4$

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

$d=\sqrt{9+9}$

$d=\sqrt{18}$

d = 4.2 units

Distance of FD:

Here, $x_1=-1, y_1=4, x_2=-1, y_2=1$

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

$d=\sqrt{9+0}$

d = 3 units

Perimeter of ΔDEF = DE + FE + FD

                                = 3 + 4.2 + 3

                                = 10.2 units

The perimeter of triangle DEF is 10.2 units.