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Lana71 [14]
3 years ago
8

What is the perimeter of triangle DEF?

Mathematics
1 answer:
Vikki [24]3 years ago
5 0

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}

<u>Distance of DE:</u>

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

<u>Distance of EF:</u>

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

<u>Distance of FD:</u>

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.

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