Atriangle with a perimeter of 66 inches has one side that is 16 inches long. the length of the other two sides have a ratio of 2: 3. what is the length, in inches, of the longest side of the triangle?

It is given in the question that,

A triangle with a perimeter of 66 inches has one side that is 16 inches long. the length of the other two sides have a ratio of 2:3.

Let the other two sides are of length 2x and 3x respectively .

And perimeter is the sum of the lengths of all three sides, that is

So the other two sides are

And the length of the longest side is 30 inches .

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer