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555-605 (Medium)|   Geometry|      
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amgelcer
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If two sides of a triangle have lengths 2 and 5 which of the following Updated on: 30 Jan 2019, 04:18
Originally posted by amgelcer on 19 Nov 2013, 03:20.
Last edited by Bunuel on 30 Jan 2019, 04:18, edited 2 times in total.
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If two sides of a triangle have lengths 2 and 5, which of the following could be the perimeter of the triangle?

I. 9
II. 15
III. 19

(A) None
(B) I only
(C) II only
(D) II and III only
(E) I, II, and III
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A
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If two sides of a triangle have lengths 2 and 5 which of the following 30 Jun 2014, 02:25
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23. Geometry




24. Coordinate Geometry




25. Triangles




26. Polygons




27. Circles




28. Rectangular Solids and Cylinders




29. Graphs and Illustrations



For other subjects:
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If two sides of a triangle have lengths 2 and 5 which of the following 19 Nov 2013, 03:29
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If two sides of a triangle have lengths 2 and 5, which of the following could be the perimeter of the triangle?

I. 9
II. 15
III. 19

(A) None
(B) I only
(C) II only
(D) II and III only
(E) I, II, and III


The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.

Therefore:

(5-2) < {third side} < (5+2).

3 < {third side} < 7.

Perimeter = {third side} + 2 + 5 = {third side} + 7.

10 < {perimeter} < 14.

Answer: A.
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If two sides of a triangle have lengths 2 and 5 which of the following 19 Nov 2013, 03:28
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Sum of two sides should be greater than the third side.
Difference between two sides should be lesser tha the third side.

So, the third side lies in the range

3 < c < 7

So perimeter lies in the range

10 < p < 14

Answer is A.
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If two sides of a triangle have lengths 2 and 5 which of the following 03 Apr 2016, 16:38
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Here is my approach => the key here is to realise that x can have any value in the range => (3,7)
So none of the options are a MATCH => A
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If two sides of a triangle have lengths 2 and 5 which of the following 27 Nov 2017, 12:19
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amgelcer
If two sides of a triangle have lengths 2 and 5, which of the following could be the perimeter of the triangle?

I. 9
II. 15
III. 19

(A) None
(B) I only
(C) II only
(D) II and III only
(E) I, II, and III
Show more

We are given that two sides of a triangle have lengths 2 and 5, and we need to determine the possible perimeter of the triangle. Here we are being tested on the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words, the sum of the lengths of the two shortest sides must be greater than the length of the longest side. Let’s evaluate the Roman numeral answer choices.

I. perimeter = 9

The two known sides sum to 7. If the perimeter is 9, then the 3rd side is 9 – 7 = 2, giving us sides of 2, 2, and 5. Since 2 + 2 = 4 is less than 5, 9 cannot be the perimeter of the triangle.

II. perimeter = 15

If the perimeter is 15, then the 3rd side is 15 – 7 = 8, giving us sides of 2, 5, and 8. Since 2 + 5 = 7 is less than 8, 15 cannot be the perimeter of the triangle.

III. perimeter = 19

If the perimeter is 19, then the 3rd side is 19 – 7 = 12 giving us sides of 2, 5, and 12. Since 2 + 5 = 7 is less than 12, 19 cannot be the perimeter of the triangle.

Answer: A
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If two sides of a triangle have lengths 2 and 5 which of the following 10 Sep 2018, 18:13
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Bunuel
amgelcer
If two sides of a triangle have lengths 2 and 5, which of the following could be the perimeter of the triangle?

I. 9
II. 15
III. 19

(A) None
(B) I only
(C) II only
(D) II and III only
(E) I, II, and III

-----------------
+KUDOS is the way to say THANKS





The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.

Therefore:
(5-2) < {third side} < (5+2).

3 < {third side} < 7.

Perimeter = {third side} + 2 + 5 = {third side} + 7.

10 < {perimeter} < 14.

Answer: A.
Show more

Bunuel, what about the case when triangle is isosceles. Why Cann't we consider 2,2 and 5 as sides or 2,5,5 sides of triangle.

Thanks,
Amm
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If two sides of a triangle have lengths 2 and 5 which of the following 10 Sep 2018, 21:02
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ammuseeru
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amgelcer
If two sides of a triangle have lengths 2 and 5, which of the following could be the perimeter of the triangle?

I. 9
II. 15
III. 19

(A) None
(B) I only
(C) II only
(D) II and III only
(E) I, II, and III

-----------------
+KUDOS is the way to say THANKS





The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.

Therefore:
(5-2) < {third side} < (5+2).

3 < {third side} < 7.

Perimeter = {third side} + 2 + 5 = {third side} + 7.

10 < {perimeter} < 14.

Answer: A.

Bunuel, what about the case when triangle is isosceles. Why Cann't we consider 2,2 and 5 as sides or 2,5,5 sides of triangle.

Thanks,
Amm
Show more

1. Sides of 2, 2, 5 won't create a triangle: 2 + 2 < 5.

2. The perimeter of {5, 5, 2} triangle is 12, which is in the range we got: 10 < {perimeter} < 14.
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If two sides of a triangle have lengths 2 and 5 which of the following 16 Aug 2020, 23:01
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the third side of ∆ would be 3<third side<7
sum of other two sides is 7
so 7+third side ; 7+4; 7+5;7+6
11,12,13
which is not given options
hence option A ; none

amgelcer
If two sides of a triangle have lengths 2 and 5, which of the following could be the perimeter of the triangle?

I. 9
II. 15
III. 19

(A) None
(B) I only
(C) II only
(D) II and III only
(E) I, II, and III
Show more
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If two sides of a triangle have lengths 2 and 5 which of the following 16 Aug 2020, 23:13
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Once you start reading the question, the first thing to strike you should be the theorem: Sum of any two sides of a triangle is greater than 3rd side.

After this, the question becomes simple enough.If the two sides are 2 and 5, the 3rd side cannot be equal to or greater than 7. Hope that helps! :)
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If two sides of a triangle have lengths 2 and 5 which of the following 17 Aug 2020, 00:44
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two sides are 2 and 5....hence the 3rd side will be less than 7 (5+2) and more than 3 (5-2) .


Hence the third side z .....3<z<7

hence perimeter should be between.....10<P<14

Option A
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If two sides of a triangle have lengths 2 and 5 which of the following 21 Oct 2023, 10:41
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A triangle has 3 sides,let’s say x,y and z
There is a rule that states x+y > z
x+z > y
z+y > x
So the sum of two sides of a triangle is always bigger than the other.
So from this,to solve the question we have the lengths 2 and 5 so we know that we need an option smaller than 2+5 = 7
There is no option smaller than 7
Answer = A

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If two sides of a triangle have lengths 2 and 5 which of the following 25 Jan 2026, 06:10
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