Which set of numbers could represent the lengths of the sides of a triangle?
A-{5, 10, 20}
B-{2, 4, 6}
C-{3, 5, 7}
D-{1, 2, 3}
Answers
Answer:
Step-by-step explanation:
{a, b, c}
a < b + c
b < a + c
c < a + b
~~~~~~~~~~~~
(A). { 5, 10, 20 } - NOT the lengths of the sides of a triangle.
20 > 5 + 10
(B). { 2, 4, 6 } - NOT the lengths of the sides of a triangle.
6 = 2 + 4
(C). { 3, 5, 7 } - Yes, the lengths of the sides of a triangle.
(D). { 1, 2, 3 } - NOT the lengths of the sides of a triangle.
3 = 1 + 2
Answer:
The correct answer is option (C){3, 5, 7}
Step-by-step explanation:
Given,
The lengths sides of the triangle.
To find,
Which does not form a triangle
Recall the concept
In a triangle, the sum of any two sides of a triangle is always greater than the third side
Solution:
In option (A), 5 +10 <20,
∵ The Sum of the two sides is not greater than the third side, {5,10,20} does not form a triangle.
In option(B), 2+4 = 6,
∵ The Sum of the two sides is not greater than the third side, {2,4,6} does not form a triangle.
In option(C), 3+5 >7, 3+7>5 and 7+5>3
∵The Sum of the two sides is greater than the third side, {3,5,7} form a triangle.
In option(D), 1+2 = 3
∵ The Sum of the two sides is not greater than the third side, {1,2,3} does not form a triangle.
Hence from the given options {3, 5, 7} form a triangle
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