Which of the following side lengths can form a triangle? a. 17 ft, 41 ft, and 60 ft b. 6 mm, 23 mm, and 88 mm c. 67 cm, 55 cm, and 121 cm d. 64 in, 65 in and 129 in

Your answer is C. 67 cm, 55 cm, and 121 cm

The rule for sides of a triangle is that any side is less than the sum of the two other sides, and greater than the difference of the two other sides. This means we can check each option and see where this applies:

A. Less than the sum of the other two sides: 17 < 41 + 60 = 101 , correct

Greater than the difference: 17 > 60 - 41 = 19 , not correct

So it's not option A.

B. Less than the sum: 6 < 88 + 23 = 111 , correct

Greater than the difference: 6 > 88 - 23 = 65 , not correct

And it's not option B.

C. Less than the sum: 67 < 55 + 121 = 176 , correct

Greater than the difference: 67 > 121 - 55 = 66 , correct

So option C fills both rules and is therefore the answer.

I hope this helps!

The sum of the lengths of any two sides of a triangle must be greater than to the length of the third side.

A.

17 + 41 = 58 < 60 NOT

B.

6 + 23 = 29 < 88 NOT

C.

67 + 55 = 123 > 121

67 + 123 = 190 > 55

55 + 123 = 178 > 67

CORRECT

D.

64 + 65 = 129 NOT

C. 67 cm, 55 cm, and 121 cm

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."