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18 Apr 2022, 23:15
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The side lengths of a given triangle are 2, 5, and \(x\). Which of the following could be the perimeter of the triangle?
I. 10
II. 12
III. 14
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III
I. 10
II. 12
III. 14
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III
PyjamaScientist
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18 Apr 2022, 23:21
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Any side of a triangle is less than the sum of the other two sides.
So,
5 + 2 > x => x < 7
2 + x > 5 = > x > 3
So, x can be 3< x < 7. Or x = 4/5/6.
Possible perimeters with these values of x = 11/12/13.
Only option (B) makes the cut.
So,
5 + 2 > x => x < 7
2 + x > 5 = > x > 3
So, x can be 3< x < 7. Or x = 4/5/6.
Possible perimeters with these values of x = 11/12/13.
Only option (B) makes the cut.
18 Apr 2022, 23:29
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Given: The side lengths of a given triangle are 2, 5, and \(x\).
Asked: Which of the following could be the perimeter of the triangle?
I. 10; x = 3; 2+3=5; straight line; Not possible
II. 12; x = 5; A triangle is possible with sides 2,5,5. POSSIBLE
III. 14; x = 7; 2+5=7; straight line; Not possible
IMO B
Posted from my mobile device
Asked: Which of the following could be the perimeter of the triangle?
I. 10; x = 3; 2+3=5; straight line; Not possible
II. 12; x = 5; A triangle is possible with sides 2,5,5. POSSIBLE
III. 14; x = 7; 2+5=7; straight line; Not possible
IMO B
Posted from my mobile device
