Which of these four sets of side lengths will form a right triangle?
2 answers:
Answer:
Set 1, Set 2, Set 3
Explanation:
In order to form a triangle:
- The longest side must be no longer than the sum of the other 2 sides
- The shortest side must be no shorter than the difference between the other 2 sides
If we call a, b, c the lengths of the 3 sides, with c = longest side and a = shortest side, this means that:
Let's now analyze the 4 sets and see if they satisfy the conditions or not:
Set 1:
a = 6 cm, b = 7 cm, c = 12 cm
We see that
12 < 6 + 7 --> OK
6 > 12 - 7 OK
So, this set can form a triangle.
Set 2:
a = 8 in, b = 29 in, c = 35 in
We see that
35 < 8 + 29 --> OK
8 > 35 - 29 --> OK
So, this set can form a triangle.
Set 3:
a = 3 mm, b = 4 mm, c = 5 mm
We see that
5 < 3+4 --> OK
3 > 5-4 --> OK
So, this set can form a triangle.
Set 4:
a = 6 ft, b = 9 ft, c = 26 ft
We see that
27 < 6 + 9 --> NO
6 > 26-9 --> NO
So, this set CANNOT form a triangle.
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