Question

Given three side lengths, select the set for which a triangle exists.
Group of answer choices

6 cm, 14 cm, 8 cm

8.5 cm, 17 cm, 10.6 cm

9 cm, 11 cm, 21 cm

14 cm, 4.7 cm, 4.7 cm

Answer 1

Are we talking about a specific triangle like a right triangle?
If so then we need to apply the Pythagorean Theorem -> a^2 + b^2 = c^2

Answer 2

What I said and then deleted since it did not say right angle

Answer 3

no

well if the order of the lengths of the legs is leg, leg, hypotenuse then yeah only of the options is right

the sum of the adjacent and opposite leg is greater than the length of the hypotenuse -- basically, just try every single one of them, and whichever turn to be right, that's your answer.

Answer 4

Lol forgot about that rule thanks @florisalreadytaken

Answer 5

Also remember, the numbers have to be in order so least to greatest

Answer 6

I am unsure if that is true.

Answer 7

Yeah they have to be or else it will be incorrect

Answer 8

None of them are labeled. They can be switched.

Answer 9

as i mentioned, if the order is ` leg, leg, hypotenuse ` then only 1 of the options is wrong -- just try them
e.g lets try a)

6 cm, 14 cm, 8 cm

\( 6+16>8 \)

that is true so that works
-- -- -- -- -- -- -- --

8.5 cm, 17 cm, 10.6 cm

\(8.5+17>10.6\)

that is true as well
-- -- -- -- -- -- -- --

9 cm, 11 cm, 21 cm

\(9+11>19\)

i dont think that works

14 cm, 4.7 cm, 4.7 cm

\(14+4.7>4.7\)

obviously, that works as well

but if the order is stated to be different please mention

Answer 10

if a,b,c are the sides of a triangle,then
1. sum of any two sides >third side.
2. difference of any two sides <third triangle.

Answer 11

only B satisfies these properties.
17-8.5=8.5<10.6

Answer 12

10.6+8.5=19.1>10.6

Answer 13

14-6=8 not less than third side
it is a triangle of zero height .
or we can say it is not a triangle.

Answer 14

mostly sum of two sides > third
but difference of two sides must be < third side for it to be a triangle.