Is it a triangle?

Level pending

Jack wants to draw a triangle such that the length of its three sides are 5 , 8 , 16 5, 8, 16 cm

Can this triangle exist?

1) Yes

2) No

3) Maybe yes, maybe no

4) There is not enough information given

4 3 2 1

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11 solutions

Trevor B.
Jan 16, 2014

By the Triangle Inequality, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, a 5 8 16 5-8-16 triangle cannot exist because 5 + 8 = 13 16. 5+8=13\not>16. The answer is 2 . \boxed{2}.

Deddy Wirata
Jan 15, 2014

For triangle that has the length of its three sides are A, B, and C. It must be fullfilled that: A + B > C A + C > B B + C > A It means that the sum of two sides must be longer than the others. You can imagine it.

Rohan Chandra
Jan 17, 2014

No way, since it is violating the Triangle Inequality Theorem that - The sum of the lengths of any two sides of a triangle must be greater than the individual length of the third side.

Raghav Dua
Jan 17, 2014

Sum of any 2 sides of a triangle must be equal to or greater than the third side. Since 5 + 8 < 16, Triangle is not possible

Dhruv Patel
Jan 16, 2014

Addition of any two sides should always exceed the remaining side. Applying this property of triangle to above example- 5+8 = 13 < 16 (remaining side)

Prasun Biswas
Feb 3, 2014

First, we should know that for a triangle to exist, the sum of any 2 sides should be greater than the third side. Here, it is said that the lengths should be 5 , 8 , 16 5,8,16 cm.

We see that ( 16 + 5 = 21 > 8 ) (16+5=21\gt 8) , ( 16 + 8 = 24 > 5 ) (16+8=24\gt 5) but ( 5 + 8 = 13 < 16 ) (5+8=13\lt 16) .

So, this triangle cannot exist.

No se completan las medidas para cerrar el triangulo aunque lo pongas de 180 grados.

Laura Lopez
Jan 27, 2014

It can't be a triangle because when you try to draw it it's impossible for the 3 sides to come together.

Muhammad Usman
Jan 18, 2014

it is necessary that the sum of two small sides should be equal to or greater then third side

Krishna Kamal
Jan 17, 2014

sum of two sides is greather than third side

Bill Czy
Jan 15, 2014

Sum of any two sides of the triangle is the limit of the other side of the triangle.

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