which set of measures could be side lengths of a triangle?
a. 4 in., 9 in., 12 in
b. 3 cm.,6 cm, 9 cm
c. 4 mm, 12, mm, 20 mm
d. 5 ft, 6 ft, 13 ft
i don't know how to get the answer so can u please explain?
I'm pretty sure you can use the Pythagorean Triples
Have you ever heard of a three four five triangle? sorry I don't think that was much help but rather a hint
no i haven't i;m only in 6th grade so can you break it down as easily as possible
A "Pythagorean Triple" is a set of positive integers, a, b and c that fits the rule:
a2 + b2 = c2
Example: The smallest Pythagorean Triple is 3, 4 and 5.
Let's check it:
32 + 42 = 52
Calculating this becomes:
9 + 16 = 25
And that is true
(3,4,5) (5,12,13) (7,24,25) (8,15,17) (9,40,41)
(11,60,61) (12,35,37) (13,84,85) (15,112,113) (16,63,65)
(17,144,145) (19,180,181) (20,21,29) (20,99,101) (21,220,221)
(23,264,265) (24,143,145) (25,312,313) (27,364,365) (28,45,53)
(28,195,197) (29,420,421) (31,480,481) (32,255,257) (33,56,65)
(33,544,545) (35,612,613) (36,77,85) (36,323,325) (37,684,685)
... infinitely many more ...
However here
the sum of any two must not be less than the third side or they will not reach
b fails
c fails
d fails
ONLY A passes :)
To determine whether a set of measures could be the side lengths of a triangle, we can use the Triangle Inequality Theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.
Let's check each option:
a. 4 in., 9 in., 12 in.
Here, the sum of the two shorter sides is 4 + 9 = 13 in, which is greater than the length of the longest side, 12 in. Thus, this set of measures could be the side lengths of a triangle.
b. 3 cm., 6 cm, 9 cm.
The sum of the two shorter sides is 3 + 6 = 9 cm, which is equal to the length of the longest side, 9 cm. According to the Triangle Inequality Theorem, the sum of the two shorter sides should be greater than the longest side, not equal to it. Therefore, this set of measures cannot be the side lengths of a triangle.
c. 4 mm, 12 mm, 20 mm.
Similar to the previous case, the sum of the two shorter sides is 4 + 12 = 16 mm, which is less than the length of the longest side, 20 mm. Therefore, this set of measures cannot be the side lengths of a triangle.
d. 5 ft, 6 ft, 13 ft.
The sum of the two shorter sides is 5 + 6 = 11 ft, which is greater than the length of the longest side, 13 ft. Thus, this set of measures could be the side lengths of a triangle.
Based on the Triangle Inequality Theorem, the sets that could be side lengths of a triangle are:
a. 4 in., 9 in., 12 in.
d. 5 ft, 6 ft, 13 ft.