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Find the perimeter RST. Round answer to the nearest tenth. Show all the work !!!

Find The Perimeter RST Round Answer To The Nearest Tenth Show All The Work class=

Sagot :

Given:

The figure of a triangle RST on a coordinate plane.

To find:

The perimeter of the triangle RST.

Solution:

From the given graph it is clear that the vertices of the given triangle are R(-2,7), S(-5,1) and T(-7,-5).

Distance formula:

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Using the distance formula, we get

[tex]RS=\sqrt{\left(-5-\left(-2\right)\right)^2+\left(1-7\right)^2}[/tex]

[tex]RS=\sqrt{\left(-5+2\right)^2+\left(1-7\right)^2}[/tex]

[tex]RS=\sqrt{\left(-3\right)^2+\left(-6\right)^2}[/tex]

on further simplification, we get

[tex]RS=\sqrt{9+36}[/tex]

[tex]RS=\sqrt{45}[/tex]

[tex]RS=3\sqrt{5}[/tex]

Similarly,

[tex]ST=\sqrt{\left(-7-\left(-5\right)\right)^2+\left(-5-1\right)^2}[/tex]

[tex]ST=2\sqrt{10}[/tex]

[tex]RT=\sqrt{\left(-7-\left(-2\right)\right)^2+\left(-5-7\right)^2}[/tex]

[tex]RT=13[/tex]

Now, the perimeter of the triangle RST is

[tex]Perimeter=RS+ST+RT[/tex]

[tex]Perimeter=3\sqrt{5}+2\sqrt{10}+13[/tex]

[tex]Perimeter=26.032759[/tex]

[tex]Perimeter\approx 26.0[/tex]

Therefore, the perimeter of the triangle RST is 26.0 units.