in the right triangular prism below, bg perpendicular fc

a right triangular prism is shown. triangles a e d and b f g are the base triangles. a perpendicular bisector is drawn from point b to point g on side f c.

the volume of the prism is 900 cubic centimeters. the height of the prism is 15 centimeters and the height of the triangular base is 10 centimeters. what is the length of edge fc?

cm

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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

the correct answer is 5 6 and 7

ratio is 2 : 9

the answer is three

13.5 : 3