Triangle RST has vertices located at R (2,3), S (4,4), and T (5,0) Part A: Find the length of each side of the triangle Show your work. Part B: Find the slope of each side of the triangle. Show your work Part C: Classify the triangle Explain your reasoning!

Distance (rounded)

RS=2

ST=4

TR=4

Slope

RS=0.5

ST=-4

TR=-1

Type of triangle

Isosceles triangle

Step-by-step explanation:

For the distance, you use the formula,

For the slope, you use the formula

Because two of the sides are the same length, we know that it is an Isosceles triangle by definition.

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Part A:  --- (Please see below in bold)

Part B: RS - Slope = 1 / 2; ST - Slope = - 4; RT - Slope = - 1

Part C: Scalene Triangle

Step-by-step explanation:

Part A:

As you can see, in the first attachment I simply potted triangle RST. In the second attachment, we come to the approach on how to determine the length of each side. Instead of applying the distance formula, I created mini right triangles with each of the sides of RST, such that all the sides were the hypotenuse of their own triangles. By now it should be clear that we can apply Pythagorean Theorem -

( RS )^2 = ( 1 )^2 + ( 2 )^2

RS = √5,

( ST )^2 = ( 1 )^2 + ( 4 )^2

ST = √17,

( RT )^2 = ( 3 )^2 + ( 3 )^2

RT = √18

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Part B:

The mini triangles that I created do come in handy to determine the slope. As it is defined as rise over run, take RS as an example. It has a "rise" of 1, as you can see, and a "run" of 2, and therefore has a slope of 1 / 2. Respectively ST has a slope of - 4, and RT has a slope of - 1.

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Part C:

When we are being asked to " classify " this triangle, I am assuming it is in terms of equilateral / scalene / isosceles. If that is so, it would be scalene, as we determined earlier that the lengths of the sides were not equal.

ad = ae + ed = y + 7

similar triangles therefor

ac/ab = ad/ae

6/4 = (y + 7) / y

cross multiply

6y = 4(y + 7)

6y = 4y + 28

2y = 28

y = 14

step-by-step explanation:

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