Question

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

Answer 1

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:

`D=√((x_2-x_1)^2+(y_2-y_1)^2)`

Using the distance formula, we get

`RS=√(\left(-5-\left(-2\right)\right)^2+\left(1-7\right)^2)`

`RS=√(\left(-5+2\right)^2+\left(1-7\right)^2)`

`RS=√(\left(-3\right)^2+\left(-6\right)^2)`

on further simplification, we get

`RS=√(9+36)`

`RS=√(45)`

`RS=3√(5)`

Similarly,

`ST=√(\left(-7-\left(-5\right)\right)^2+\left(-5-1\right)^2)`

`ST=2√(10)`

`RT=√(\left(-7-\left(-2\right)\right)^2+\left(-5-7\right)^2)`

`RT=13`

Now, the perimeter of the triangle RST is

`Perimeter=RS+ST+RT`

`Perimeter=3√(5)+2√(10)+13`

`Perimeter=26.032759`

`Perimeter\approx 26.0`

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