Determine if each set of given side lengths can be used to construct a triangle. Select all that apply.
a. 1 mm, 2 mm, 3 mm
b. 5 cm, 8 cm, 12 cm
c. 12 in, 12 in, 12 in
d. 3 ft, 6 ft, 10 ft
e. 6 m, 10 m, 15 m
for any triangle with sides a,b,c where c is the longest side, you must have
c < a+b
So (e) works, because 15 < 6+10
Now try the others.
To determine whether a set of side lengths can be used to construct a triangle, we need to check if the sum of any two sides is greater than the third side. If this condition is true for all three pairs of sides, then a triangle can be formed. Let's go through each set of side lengths:
a. 1 mm, 2 mm, 3 mm
Here, the sum of the two shorter sides (1 mm + 2 mm = 3 mm) is equal to the length of the longest side (3 mm). In this case, a triangle can be formed.
b. 5 cm, 8 cm, 12 cm
Let's check if the condition holds true in this case. The sum of the two shorter sides (5 cm + 8 cm = 13 cm) is greater than the length of the longest side (12 cm), so a triangle can be formed.
c. 12 in, 12 in, 12 in
In this case, all three side lengths are equal, which means it is an equilateral triangle. Since the sum of any two sides (12 in + 12 in = 24 in) is always greater than the length of the remaining side (12 in), a triangle can be formed.
d. 3 ft, 6 ft, 10 ft
Let's check the condition. The sum of the two shorter sides (3 ft + 6 ft = 9 ft) is less than the length of the longest side (10 ft). This means that a triangle cannot be formed.
e. 6 m, 10 m, 15 m
To check this set of side lengths, we find that the sum of the two shorter sides (6 m + 10 m = 16 m) is greater than the length of the longest side (15 m). Therefore, a triangle can be formed.
So, the sets of side lengths that can be used to construct a triangle are:
a. 1 mm, 2 mm, 3 mm
b. 5 cm, 8 cm, 12 cm
c. 12 in, 12 in, 12 in
e. 6 m, 10 m, 15 m