Question

Which set of numbers may represent the lengths of the sides of a triangle? (A) {2,5,9} (B) {6,6,7} (C) {6,4,2} (D) {7,8,1}

Answer 1

B {6, 6, 7}

Explanation:

Which set of numbers may represent the lengths of the sides of a triangle? (A) {2,5,9} (B) {6,6,7} (C) {6,4,2} (D) {7,8,1}

For a given triangle with 3 sides, the sun of the length of any two sides must be greater Than the third side. This can be expressed mathematically as;

Let the side be ;

x, y and z

Then:

x > (y + z) or

y > (x + z) or

z > (x + y)

For A{2,5,9}

(2 + 5) < 9 (does not meet criteria)

For B {6,6,7}

(6 +6) > 7

(7 +6) > 6

Meets all criteria

For C {6,4,2}

(4 +2) is not greater Than 6 (does not meet criteria)

For D {7,8,1}

(7 +1) is not greater Than 8 ( does not meet criteria)